Random walk in a high density dynamic random environment
The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibr...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
den Hollander, Frank [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2014transfer abstract |
|---|
| Schlagwörter: |
|---|
| Umfang: |
15 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Optical and white light emission properties of Dy - Babu, P. ELSEVIER, 2021, Amsterdam |
|---|---|
| Übergeordnetes Werk: |
volume:25 ; year:2014 ; number:4 ; day:27 ; month:06 ; pages:785-799 ; extent:15 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.indag.2014.04.010 |
|---|
| Katalog-ID: |
ELV039537668 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | ELV039537668 | ||
| 003 | DE-627 | ||
| 005 | 20230625225210.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 180603s2014 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.indag.2014.04.010 |2 doi | |
| 028 | 5 | 2 | |a GBVA2014021000005.pica |
| 035 | |a (DE-627)ELV039537668 | ||
| 035 | |a (ELSEVIER)S0019-3577(14)00039-1 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | |a 510 | |
| 082 | 0 | 4 | |a 510 |q DE-600 |
| 082 | 0 | 4 | |a 530 |q VZ |
| 084 | |a 33.60 |2 bkl | ||
| 084 | |a 51.00 |2 bkl | ||
| 100 | 1 | |a den Hollander, Frank |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Random walk in a high density dynamic random environment |
| 264 | 1 | |c 2014transfer abstract | |
| 300 | |a 15 | ||
| 336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
| 337 | |a nicht spezifiziert |b z |2 rdamedia | ||
| 338 | |a nicht spezifiziert |b zu |2 rdacarrier | ||
| 520 | |a The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. | ||
| 520 | |a The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. | ||
| 650 | 7 | |a Dynamic random environment |2 Elsevier | |
| 650 | 7 | |a Random walk |2 Elsevier | |
| 650 | 7 | |a Law of large numbers |2 Elsevier | |
| 650 | 7 | |a Multi-scale renormalization |2 Elsevier | |
| 700 | 1 | |a Kesten, Harry |4 oth | |
| 700 | 1 | |a Sidoravicius, Vladas |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a Babu, P. ELSEVIER |t Optical and white light emission properties of Dy |d 2021 |g Amsterdam |w (DE-627)ELV006009107 |
| 773 | 1 | 8 | |g volume:25 |g year:2014 |g number:4 |g day:27 |g month:06 |g pages:785-799 |g extent:15 |
| 856 | 4 | 0 | |u https://doi.org/10.1016/j.indag.2014.04.010 |3 Volltext |
| 912 | |a GBV_USEFLAG_U | ||
| 912 | |a GBV_ELV | ||
| 912 | |a SYSFLAG_U | ||
| 936 | b | k | |a 33.60 |j Kondensierte Materie: Allgemeines |q VZ |
| 936 | b | k | |a 51.00 |j Werkstoffkunde: Allgemeines |q VZ |
| 951 | |a AR | ||
| 952 | |d 25 |j 2014 |e 4 |b 27 |c 0627 |h 785-799 |g 15 | ||
| 953 | |2 045F |a 510 | ||
| author_variant |
h f d hf hfd |
|---|---|
| matchkey_str |
denhollanderfrankkestenharrysidoravicius:2014----:admaknhgdniyyairno |
| hierarchy_sort_str |
2014transfer abstract |
| bklnumber |
33.60 51.00 |
| publishDate |
2014 |
| allfields |
10.1016/j.indag.2014.04.010 doi GBVA2014021000005.pica (DE-627)ELV039537668 (ELSEVIER)S0019-3577(14)00039-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl den Hollander, Frank verfasserin aut Random walk in a high density dynamic random environment 2014transfer abstract 15 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Elsevier Kesten, Harry oth Sidoravicius, Vladas oth Enthalten in Elsevier Babu, P. ELSEVIER Optical and white light emission properties of Dy 2021 Amsterdam (DE-627)ELV006009107 volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 https://doi.org/10.1016/j.indag.2014.04.010 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.60 Kondensierte Materie: Allgemeines VZ 51.00 Werkstoffkunde: Allgemeines VZ AR 25 2014 4 27 0627 785-799 15 045F 510 |
| spelling |
10.1016/j.indag.2014.04.010 doi GBVA2014021000005.pica (DE-627)ELV039537668 (ELSEVIER)S0019-3577(14)00039-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl den Hollander, Frank verfasserin aut Random walk in a high density dynamic random environment 2014transfer abstract 15 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Elsevier Kesten, Harry oth Sidoravicius, Vladas oth Enthalten in Elsevier Babu, P. ELSEVIER Optical and white light emission properties of Dy 2021 Amsterdam (DE-627)ELV006009107 volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 https://doi.org/10.1016/j.indag.2014.04.010 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.60 Kondensierte Materie: Allgemeines VZ 51.00 Werkstoffkunde: Allgemeines VZ AR 25 2014 4 27 0627 785-799 15 045F 510 |
| allfields_unstemmed |
10.1016/j.indag.2014.04.010 doi GBVA2014021000005.pica (DE-627)ELV039537668 (ELSEVIER)S0019-3577(14)00039-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl den Hollander, Frank verfasserin aut Random walk in a high density dynamic random environment 2014transfer abstract 15 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Elsevier Kesten, Harry oth Sidoravicius, Vladas oth Enthalten in Elsevier Babu, P. ELSEVIER Optical and white light emission properties of Dy 2021 Amsterdam (DE-627)ELV006009107 volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 https://doi.org/10.1016/j.indag.2014.04.010 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.60 Kondensierte Materie: Allgemeines VZ 51.00 Werkstoffkunde: Allgemeines VZ AR 25 2014 4 27 0627 785-799 15 045F 510 |
| allfieldsGer |
10.1016/j.indag.2014.04.010 doi GBVA2014021000005.pica (DE-627)ELV039537668 (ELSEVIER)S0019-3577(14)00039-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl den Hollander, Frank verfasserin aut Random walk in a high density dynamic random environment 2014transfer abstract 15 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Elsevier Kesten, Harry oth Sidoravicius, Vladas oth Enthalten in Elsevier Babu, P. ELSEVIER Optical and white light emission properties of Dy 2021 Amsterdam (DE-627)ELV006009107 volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 https://doi.org/10.1016/j.indag.2014.04.010 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.60 Kondensierte Materie: Allgemeines VZ 51.00 Werkstoffkunde: Allgemeines VZ AR 25 2014 4 27 0627 785-799 15 045F 510 |
| allfieldsSound |
10.1016/j.indag.2014.04.010 doi GBVA2014021000005.pica (DE-627)ELV039537668 (ELSEVIER)S0019-3577(14)00039-1 DE-627 ger DE-627 rakwb eng 510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl den Hollander, Frank verfasserin aut Random walk in a high density dynamic random environment 2014transfer abstract 15 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Elsevier Kesten, Harry oth Sidoravicius, Vladas oth Enthalten in Elsevier Babu, P. ELSEVIER Optical and white light emission properties of Dy 2021 Amsterdam (DE-627)ELV006009107 volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 https://doi.org/10.1016/j.indag.2014.04.010 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.60 Kondensierte Materie: Allgemeines VZ 51.00 Werkstoffkunde: Allgemeines VZ AR 25 2014 4 27 0627 785-799 15 045F 510 |
| language |
English |
| source |
Enthalten in Optical and white light emission properties of Dy Amsterdam volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 |
| sourceStr |
Enthalten in Optical and white light emission properties of Dy Amsterdam volume:25 year:2014 number:4 day:27 month:06 pages:785-799 extent:15 |
| format_phy_str_mv |
Article |
| bklname |
Kondensierte Materie: Allgemeines Werkstoffkunde: Allgemeines |
| institution |
findex.gbv.de |
| topic_facet |
Dynamic random environment Random walk Law of large numbers Multi-scale renormalization |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Optical and white light emission properties of Dy |
| authorswithroles_txt_mv |
den Hollander, Frank @@aut@@ Kesten, Harry @@oth@@ Sidoravicius, Vladas @@oth@@ |
| publishDateDaySort_date |
2014-01-27T00:00:00Z |
| hierarchy_top_id |
ELV006009107 |
| dewey-sort |
3510 |
| id |
ELV039537668 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV039537668</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625225210.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2014 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.indag.2014.04.010</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2014021000005.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV039537668</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0019-3577(14)00039-1</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.60</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">51.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">den Hollander, Frank</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random walk in a high density dynamic random environment</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">15</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Dynamic random environment</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Random walk</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Law of large numbers</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Multi-scale renormalization</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kesten, Harry</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sidoravicius, Vladas</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="a">Babu, P. ELSEVIER</subfield><subfield code="t">Optical and white light emission properties of Dy</subfield><subfield code="d">2021</subfield><subfield code="g">Amsterdam</subfield><subfield code="w">(DE-627)ELV006009107</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:25</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:4</subfield><subfield code="g">day:27</subfield><subfield code="g">month:06</subfield><subfield code="g">pages:785-799</subfield><subfield code="g">extent:15</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.indag.2014.04.010</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">33.60</subfield><subfield code="j">Kondensierte Materie: Allgemeines</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">51.00</subfield><subfield code="j">Werkstoffkunde: Allgemeines</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">25</subfield><subfield code="j">2014</subfield><subfield code="e">4</subfield><subfield code="b">27</subfield><subfield code="c">0627</subfield><subfield code="h">785-799</subfield><subfield code="g">15</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
| author |
den Hollander, Frank |
| spellingShingle |
den Hollander, Frank ddc 510 ddc 530 bkl 33.60 bkl 51.00 Elsevier Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Random walk in a high density dynamic random environment |
| authorStr |
den Hollander, Frank |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)ELV006009107 |
| format |
electronic Article |
| dewey-ones |
510 - Mathematics 530 - Physics |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
elsevier |
| remote_str |
true |
| illustrated |
Not Illustrated |
| topic_title |
510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl Random walk in a high density dynamic random environment Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization Elsevier |
| topic |
ddc 510 ddc 530 bkl 33.60 bkl 51.00 Elsevier Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization |
| topic_unstemmed |
ddc 510 ddc 530 bkl 33.60 bkl 51.00 Elsevier Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization |
| topic_browse |
ddc 510 ddc 530 bkl 33.60 bkl 51.00 Elsevier Dynamic random environment Elsevier Random walk Elsevier Law of large numbers Elsevier Multi-scale renormalization |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
zu |
| author2_variant |
h k hk v s vs |
| hierarchy_parent_title |
Optical and white light emission properties of Dy |
| hierarchy_parent_id |
ELV006009107 |
| dewey-tens |
510 - Mathematics 530 - Physics |
| hierarchy_top_title |
Optical and white light emission properties of Dy |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)ELV006009107 |
| title |
Random walk in a high density dynamic random environment |
| ctrlnum |
(DE-627)ELV039537668 (ELSEVIER)S0019-3577(14)00039-1 |
| title_full |
Random walk in a high density dynamic random environment |
| author_sort |
den Hollander, Frank |
| journal |
Optical and white light emission properties of Dy |
| journalStr |
Optical and white light emission properties of Dy |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2014 |
| contenttype_str_mv |
zzz |
| container_start_page |
785 |
| author_browse |
den Hollander, Frank |
| container_volume |
25 |
| physical |
15 |
| class |
510 510 DE-600 530 VZ 33.60 bkl 51.00 bkl |
| format_se |
Elektronische Aufsätze |
| author-letter |
den Hollander, Frank |
| doi_str_mv |
10.1016/j.indag.2014.04.010 |
| dewey-full |
510 530 |
| title_sort |
random walk in a high density dynamic random environment |
| title_auth |
Random walk in a high density dynamic random environment |
| abstract |
The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. |
| abstractGer |
The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. |
| abstract_unstemmed |
The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain. |
| collection_details |
GBV_USEFLAG_U GBV_ELV SYSFLAG_U |
| container_issue |
4 |
| title_short |
Random walk in a high density dynamic random environment |
| url |
https://doi.org/10.1016/j.indag.2014.04.010 |
| remote_bool |
true |
| author2 |
Kesten, Harry Sidoravicius, Vladas |
| author2Str |
Kesten, Harry Sidoravicius, Vladas |
| ppnlink |
ELV006009107 |
| mediatype_str_mv |
z |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth oth |
| doi_str |
10.1016/j.indag.2014.04.010 |
| up_date |
2024-07-06T20:52:00.052Z |
| _version_ |
1803864370107645952 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV039537668</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625225210.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2014 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.indag.2014.04.010</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2014021000005.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV039537668</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0019-3577(14)00039-1</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.60</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">51.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">den Hollander, Frank</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random walk in a high density dynamic random environment</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">15</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z d , d ≥ 1 . The red particles jump at rate 1 and are in a Poisson equilibrium with density μ . The green particle also jumps at rate 1, but uses different transition kernels p ′ and p ″ depending on whether it sees a red particle or not. It is shown that, in the limit as μ → ∞ , the speed of the green particle tends to the average jump under p ′ . This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Dynamic random environment</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Random walk</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Law of large numbers</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Multi-scale renormalization</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kesten, Harry</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sidoravicius, Vladas</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="a">Babu, P. ELSEVIER</subfield><subfield code="t">Optical and white light emission properties of Dy</subfield><subfield code="d">2021</subfield><subfield code="g">Amsterdam</subfield><subfield code="w">(DE-627)ELV006009107</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:25</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:4</subfield><subfield code="g">day:27</subfield><subfield code="g">month:06</subfield><subfield code="g">pages:785-799</subfield><subfield code="g">extent:15</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.indag.2014.04.010</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">33.60</subfield><subfield code="j">Kondensierte Materie: Allgemeines</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">51.00</subfield><subfield code="j">Werkstoffkunde: Allgemeines</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">25</subfield><subfield code="j">2014</subfield><subfield code="e">4</subfield><subfield code="b">27</subfield><subfield code="c">0627</subfield><subfield code="h">785-799</subfield><subfield code="g">15</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
| score |
7.399296 |