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February 2021 Derivation of viscous Burgers equations from weakly asymmetric exclusion processes
M. Jara, C. Landim, K. Tsunoda
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Ann. Inst. H. Poincaré Probab. Statist. 57(1): 169-194 (February 2021). DOI: 10.1214/20-AIHP1075

Abstract

We consider weakly asymmetric exclusion processes whose initial density profile is a small perturbation of a constant. We show that in the diffusive time-scale, in all dimensions, the density defect evolves as the solution of a viscous Burgers equation.

Nous examinons le processus d’exclusion simple faiblement asymétrique partant d’une perturbation d’un profil de densité constant. Nous montrons qu’à l’échelle diffusive, en toute dimension, la perturbation évolue selon la solution d’une équation de Burgers visqueuse.

Acknowledgements

Part of this work was done during K. Tsunoda’s visit to IMPA. He would like to thank IMPA for numerous support and warm hospitality during his visit. M. Jara acknowledges CNPq for its support through the Grant 305075/2017-9, FAPERJ for its support through the Grant E-29/203.012/2018 and ERC for its support through the European Unions Horizon 2020 research and innovative programme (Grant Agreement No. 715734). C. Landim has been partially supported by FAPERJ CNE E-26/201.207/2014, by CNPq Bolsa de Produtividade em Pesquisa PQ 303538/2014-7, and by ANR-15-CE40-0020-01 LSD of the French National Research Agency. K. Tsunoda has been partially supported by JSPS KAKENHI, Grant-in-Aid for Early-Career Scientists 18K13426. The authors are grateful to the anonymous referees for the careful reading and their comments.

Citation

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M. Jara. C. Landim. K. Tsunoda. "Derivation of viscous Burgers equations from weakly asymmetric exclusion processes." Ann. Inst. H. Poincaré Probab. Statist. 57 (1) 169 - 194, February 2021. https://doi.org/10.1214/20-AIHP1075

Information

Received: 19 July 2019; Revised: 26 May 2020; Accepted: 29 May 2020; Published: February 2021
First available in Project Euclid: 12 March 2021

Digital Object Identifier: 10.1214/20-AIHP1075

Subjects:
Primary: 60K35
Secondary: 82C22

Keywords: Incompressible limits , Viscous Burgers equations , Weakly asymmetric exclusion processes

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

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Vol.57 • No. 1 • February 2021
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