Statistical Properties of Eigenvalues of Laplace–Beltrami Operators
Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restric...
Ausführliche Beschreibung
Autor*in: |
Jiang, Tiefeng [verfasserIn] |
---|
Format: |
Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2021 |
---|
Schlagwörter: |
---|
Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2021 |
---|
Übergeordnetes Werk: |
Enthalten in: Journal of theoretical probability - Springer US, 1988, 34(2021), 3 vom: 01. Jan., Seite 1061-1109 |
---|---|
Übergeordnetes Werk: |
volume:34 ; year:2021 ; number:3 ; day:01 ; month:01 ; pages:1061-1109 |
Links: |
---|
DOI / URN: |
10.1007/s10959-020-01061-6 |
---|
Katalog-ID: |
OLC2126787834 |
---|
LEADER | 01000naa a22002652 4500 | ||
---|---|---|---|
001 | OLC2126787834 | ||
003 | DE-627 | ||
005 | 20230505121419.0 | ||
007 | tu | ||
008 | 230505s2021 xx ||||| 00| ||eng c | ||
024 | 7 | |a 10.1007/s10959-020-01061-6 |2 doi | |
035 | |a (DE-627)OLC2126787834 | ||
035 | |a (DE-He213)s10959-020-01061-6-p | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
082 | 0 | 4 | |a 510 |q VZ |
084 | |a 17,1 |2 ssgn | ||
100 | 1 | |a Jiang, Tiefeng |e verfasserin |4 aut | |
245 | 1 | 0 | |a Statistical Properties of Eigenvalues of Laplace–Beltrami Operators |
264 | 1 | |c 2021 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
338 | |a Band |b nc |2 rdacarrier | ||
500 | |a © Springer Science+Business Media, LLC, part of Springer Nature 2021 | ||
520 | |a Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. | ||
650 | 4 | |a Laplace–Beltrami operator | |
650 | 4 | |a Eigenvalue | |
650 | 4 | |a Random partition | |
650 | 4 | |a Plancherel measure | |
650 | 4 | |a Uniform measure | |
650 | 4 | |a Restricted Jack measure | |
650 | 4 | |a Restricted uniform measure | |
650 | 4 | |a Tracy–Widom distribution | |
650 | 4 | |a Gumbel distribution | |
650 | 4 | |a Gamma distribution | |
700 | 1 | |a Wang, Ke |0 (orcid)0000-0001-8128-3441 |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Journal of theoretical probability |d Springer US, 1988 |g 34(2021), 3 vom: 01. Jan., Seite 1061-1109 |w (DE-627)129930903 |w (DE-600)357043-5 |w (DE-576)018191886 |x 0894-9840 |7 nnns |
773 | 1 | 8 | |g volume:34 |g year:2021 |g number:3 |g day:01 |g month:01 |g pages:1061-1109 |
856 | 4 | 1 | |u https://doi.org/10.1007/s10959-020-01061-6 |z lizenzpflichtig |3 Volltext |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_OLC | ||
912 | |a SSG-OLC-MAT | ||
912 | |a SSG-OPC-MAT | ||
912 | |a GBV_ILN_4027 | ||
951 | |a AR | ||
952 | |d 34 |j 2021 |e 3 |b 01 |c 01 |h 1061-1109 |
author_variant |
t j tj k w kw |
---|---|
matchkey_str |
article:08949840:2021----::ttsiapoeteoegnausfalcb |
hierarchy_sort_str |
2021 |
publishDate |
2021 |
allfields |
10.1007/s10959-020-01061-6 doi (DE-627)OLC2126787834 (DE-He213)s10959-020-01061-6-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jiang, Tiefeng verfasserin aut Statistical Properties of Eigenvalues of Laplace–Beltrami Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution Wang, Ke (orcid)0000-0001-8128-3441 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2021), 3 vom: 01. Jan., Seite 1061-1109 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 https://doi.org/10.1007/s10959-020-01061-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2021 3 01 01 1061-1109 |
spelling |
10.1007/s10959-020-01061-6 doi (DE-627)OLC2126787834 (DE-He213)s10959-020-01061-6-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jiang, Tiefeng verfasserin aut Statistical Properties of Eigenvalues of Laplace–Beltrami Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution Wang, Ke (orcid)0000-0001-8128-3441 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2021), 3 vom: 01. Jan., Seite 1061-1109 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 https://doi.org/10.1007/s10959-020-01061-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2021 3 01 01 1061-1109 |
allfields_unstemmed |
10.1007/s10959-020-01061-6 doi (DE-627)OLC2126787834 (DE-He213)s10959-020-01061-6-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jiang, Tiefeng verfasserin aut Statistical Properties of Eigenvalues of Laplace–Beltrami Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution Wang, Ke (orcid)0000-0001-8128-3441 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2021), 3 vom: 01. Jan., Seite 1061-1109 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 https://doi.org/10.1007/s10959-020-01061-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2021 3 01 01 1061-1109 |
allfieldsGer |
10.1007/s10959-020-01061-6 doi (DE-627)OLC2126787834 (DE-He213)s10959-020-01061-6-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jiang, Tiefeng verfasserin aut Statistical Properties of Eigenvalues of Laplace–Beltrami Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution Wang, Ke (orcid)0000-0001-8128-3441 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2021), 3 vom: 01. Jan., Seite 1061-1109 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 https://doi.org/10.1007/s10959-020-01061-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2021 3 01 01 1061-1109 |
allfieldsSound |
10.1007/s10959-020-01061-6 doi (DE-627)OLC2126787834 (DE-He213)s10959-020-01061-6-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jiang, Tiefeng verfasserin aut Statistical Properties of Eigenvalues of Laplace–Beltrami Operators 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution Wang, Ke (orcid)0000-0001-8128-3441 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2021), 3 vom: 01. Jan., Seite 1061-1109 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 https://doi.org/10.1007/s10959-020-01061-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2021 3 01 01 1061-1109 |
language |
English |
source |
Enthalten in Journal of theoretical probability 34(2021), 3 vom: 01. Jan., Seite 1061-1109 volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 |
sourceStr |
Enthalten in Journal of theoretical probability 34(2021), 3 vom: 01. Jan., Seite 1061-1109 volume:34 year:2021 number:3 day:01 month:01 pages:1061-1109 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
topic_facet |
Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution |
dewey-raw |
510 |
isfreeaccess_bool |
false |
container_title |
Journal of theoretical probability |
authorswithroles_txt_mv |
Jiang, Tiefeng @@aut@@ Wang, Ke @@aut@@ |
publishDateDaySort_date |
2021-01-01T00:00:00Z |
hierarchy_top_id |
129930903 |
dewey-sort |
3510 |
id |
OLC2126787834 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2126787834</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505121419.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10959-020-01061-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2126787834</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10959-020-01061-6-p</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="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jiang, Tiefeng</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Statistical Properties of Eigenvalues of Laplace–Beltrami Operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC, part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Laplace–Beltrami operator</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenvalue</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random partition</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Plancherel measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Uniform measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted Jack measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted uniform measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tracy–Widom distribution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gumbel distribution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gamma distribution</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wang, Ke</subfield><subfield code="0">(orcid)0000-0001-8128-3441</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of theoretical probability</subfield><subfield code="d">Springer US, 1988</subfield><subfield code="g">34(2021), 3 vom: 01. Jan., Seite 1061-1109</subfield><subfield code="w">(DE-627)129930903</subfield><subfield code="w">(DE-600)357043-5</subfield><subfield code="w">(DE-576)018191886</subfield><subfield code="x">0894-9840</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:34</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:3</subfield><subfield code="g">day:01</subfield><subfield code="g">month:01</subfield><subfield code="g">pages:1061-1109</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10959-020-01061-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4027</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">34</subfield><subfield code="j">2021</subfield><subfield code="e">3</subfield><subfield code="b">01</subfield><subfield code="c">01</subfield><subfield code="h">1061-1109</subfield></datafield></record></collection>
|
author |
Jiang, Tiefeng |
spellingShingle |
Jiang, Tiefeng ddc 510 ssgn 17,1 misc Laplace–Beltrami operator misc Eigenvalue misc Random partition misc Plancherel measure misc Uniform measure misc Restricted Jack measure misc Restricted uniform measure misc Tracy–Widom distribution misc Gumbel distribution misc Gamma distribution Statistical Properties of Eigenvalues of Laplace–Beltrami Operators |
authorStr |
Jiang, Tiefeng |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)129930903 |
format |
Article |
dewey-ones |
510 - Mathematics |
delete_txt_mv |
keep |
author_role |
aut aut |
collection |
OLC |
remote_str |
false |
illustrated |
Not Illustrated |
issn |
0894-9840 |
topic_title |
510 VZ 17,1 ssgn Statistical Properties of Eigenvalues of Laplace–Beltrami Operators Laplace–Beltrami operator Eigenvalue Random partition Plancherel measure Uniform measure Restricted Jack measure Restricted uniform measure Tracy–Widom distribution Gumbel distribution Gamma distribution |
topic |
ddc 510 ssgn 17,1 misc Laplace–Beltrami operator misc Eigenvalue misc Random partition misc Plancherel measure misc Uniform measure misc Restricted Jack measure misc Restricted uniform measure misc Tracy–Widom distribution misc Gumbel distribution misc Gamma distribution |
topic_unstemmed |
ddc 510 ssgn 17,1 misc Laplace–Beltrami operator misc Eigenvalue misc Random partition misc Plancherel measure misc Uniform measure misc Restricted Jack measure misc Restricted uniform measure misc Tracy–Widom distribution misc Gumbel distribution misc Gamma distribution |
topic_browse |
ddc 510 ssgn 17,1 misc Laplace–Beltrami operator misc Eigenvalue misc Random partition misc Plancherel measure misc Uniform measure misc Restricted Jack measure misc Restricted uniform measure misc Tracy–Widom distribution misc Gumbel distribution misc Gamma distribution |
format_facet |
Aufsätze Gedruckte Aufsätze |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
nc |
hierarchy_parent_title |
Journal of theoretical probability |
hierarchy_parent_id |
129930903 |
dewey-tens |
510 - Mathematics |
hierarchy_top_title |
Journal of theoretical probability |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 |
title |
Statistical Properties of Eigenvalues of Laplace–Beltrami Operators |
ctrlnum |
(DE-627)OLC2126787834 (DE-He213)s10959-020-01061-6-p |
title_full |
Statistical Properties of Eigenvalues of Laplace–Beltrami Operators |
author_sort |
Jiang, Tiefeng |
journal |
Journal of theoretical probability |
journalStr |
Journal of theoretical probability |
lang_code |
eng |
isOA_bool |
false |
dewey-hundreds |
500 - Science |
recordtype |
marc |
publishDateSort |
2021 |
contenttype_str_mv |
txt |
container_start_page |
1061 |
author_browse |
Jiang, Tiefeng Wang, Ke |
container_volume |
34 |
class |
510 VZ 17,1 ssgn |
format_se |
Aufsätze |
author-letter |
Jiang, Tiefeng |
doi_str_mv |
10.1007/s10959-020-01061-6 |
normlink |
(ORCID)0000-0001-8128-3441 |
normlink_prefix_str_mv |
(orcid)0000-0001-8128-3441 |
dewey-full |
510 |
title_sort |
statistical properties of eigenvalues of laplace–beltrami operators |
title_auth |
Statistical Properties of Eigenvalues of Laplace–Beltrami Operators |
abstract |
Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. © Springer Science+Business Media, LLC, part of Springer Nature 2021 |
abstractGer |
Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. © Springer Science+Business Media, LLC, part of Springer Nature 2021 |
abstract_unstemmed |
Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked. © Springer Science+Business Media, LLC, part of Springer Nature 2021 |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 |
container_issue |
3 |
title_short |
Statistical Properties of Eigenvalues of Laplace–Beltrami Operators |
url |
https://doi.org/10.1007/s10959-020-01061-6 |
remote_bool |
false |
author2 |
Wang, Ke |
author2Str |
Wang, Ke |
ppnlink |
129930903 |
mediatype_str_mv |
n |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1007/s10959-020-01061-6 |
up_date |
2024-07-04T08:24:41.870Z |
_version_ |
1803636159933317120 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2126787834</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505121419.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10959-020-01061-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2126787834</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10959-020-01061-6-p</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="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jiang, Tiefeng</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Statistical Properties of Eigenvalues of Laplace–Beltrami Operators</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC, part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study the eigenvalues of a Laplace–Beltrami operator defined on the set of the symmetric polynomials, where the eigenvalues are expressed in terms of partitions of integers. To study the behaviors of these eigenvalues, we assign partitions with the restricted uniform measure, the restricted Jack measure, the uniform measure, or the Plancherel measure. We first obtain a new limit theorem on the restricted uniform measure. Then, by using it together with known results on other three measures, we prove that the global distribution of the eigenvalues is asymptotically a new distribution $$\mu $$, the Gamma distribution, the Gumbel distribution, and the Tracy–Widom distribution, respectively. The Tracy–Widom distribution is obtained for a special case only due to a technical constraint. An explicit representation of $$\mu $$ is obtained by a function of independent random variables. Two open problems are also asked.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Laplace–Beltrami operator</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenvalue</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random partition</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Plancherel measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Uniform measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted Jack measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted uniform measure</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tracy–Widom distribution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gumbel distribution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gamma distribution</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wang, Ke</subfield><subfield code="0">(orcid)0000-0001-8128-3441</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of theoretical probability</subfield><subfield code="d">Springer US, 1988</subfield><subfield code="g">34(2021), 3 vom: 01. Jan., Seite 1061-1109</subfield><subfield code="w">(DE-627)129930903</subfield><subfield code="w">(DE-600)357043-5</subfield><subfield code="w">(DE-576)018191886</subfield><subfield code="x">0894-9840</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:34</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:3</subfield><subfield code="g">day:01</subfield><subfield code="g">month:01</subfield><subfield code="g">pages:1061-1109</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10959-020-01061-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4027</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">34</subfield><subfield code="j">2021</subfield><subfield code="e">3</subfield><subfield code="b">01</subfield><subfield code="c">01</subfield><subfield code="h">1061-1109</subfield></datafield></record></collection>
|
score |
7.4013853 |