Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models
Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions....
Ausführliche Beschreibung
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| Autor*in: |
Tóth, Bálint [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2002 |
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| Anmerkung: |
© Plenum Publishing Corporation 2002 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of statistical physics - Kluwer Academic Publishers-Plenum Publishers, 1969, 109(2002), 1-2 vom: Okt., Seite 177-205 |
|---|---|
| Übergeordnetes Werk: |
volume:109 ; year:2002 ; number:1-2 ; month:10 ; pages:177-205 |
| Links: |
|---|
| DOI / URN: |
10.1023/A:1019987628197 |
|---|
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OLC2046598199 |
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| 520 | |a Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. | ||
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10.1023/A:1019987628197 doi (DE-627)OLC2046598199 (DE-He213)A:1019987628197-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Tóth, Bálint verfasserin aut Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 2002 Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. Valkó, Benedek aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 109(2002), 1-2 vom: Okt., Seite 177-205 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:109 year:2002 number:1-2 month:10 pages:177-205 https://doi.org/10.1023/A:1019987628197 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4323 33.00 VZ AR 109 2002 1-2 10 177-205 |
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10.1023/A:1019987628197 doi (DE-627)OLC2046598199 (DE-He213)A:1019987628197-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Tóth, Bálint verfasserin aut Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 2002 Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. Valkó, Benedek aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 109(2002), 1-2 vom: Okt., Seite 177-205 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:109 year:2002 number:1-2 month:10 pages:177-205 https://doi.org/10.1023/A:1019987628197 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4323 33.00 VZ AR 109 2002 1-2 10 177-205 |
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10.1023/A:1019987628197 doi (DE-627)OLC2046598199 (DE-He213)A:1019987628197-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Tóth, Bálint verfasserin aut Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 2002 Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. Valkó, Benedek aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 109(2002), 1-2 vom: Okt., Seite 177-205 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:109 year:2002 number:1-2 month:10 pages:177-205 https://doi.org/10.1023/A:1019987628197 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4323 33.00 VZ AR 109 2002 1-2 10 177-205 |
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10.1023/A:1019987628197 doi (DE-627)OLC2046598199 (DE-He213)A:1019987628197-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Tóth, Bálint verfasserin aut Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models 2002 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 2002 Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. Valkó, Benedek aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 109(2002), 1-2 vom: Okt., Seite 177-205 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:109 year:2002 number:1-2 month:10 pages:177-205 https://doi.org/10.1023/A:1019987628197 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2409 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4323 33.00 VZ AR 109 2002 1-2 10 177-205 |
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between equilibrium fluctuations and eulerian scaling: perturbation of equilibrium for a class of deposition models |
| title_auth |
Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models |
| abstract |
Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. © Plenum Publishing Corporation 2002 |
| abstractGer |
Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. © Plenum Publishing Corporation 2002 |
| abstract_unstemmed |
Abstract We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, “bricklayers” models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<β<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N1+β, the macroscopic evolution of perturbations of microscopic order N−β of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<β<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for β≥1/5. © Plenum Publishing Corporation 2002 |
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| title_short |
Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models |
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Valkó, Benedek |
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