QUANTITATIVE HOMOGENIZATION OF INTERACTING PARTICLE SYSTEMS

Arianna Giunti; Chenlin Gu; Jean Christophe Mourrat

doi:10.1214/22-AOP1573

QUANTITATIVE HOMOGENIZATION OF INTERACTING PARTICLE SYSTEMS

Arianna Giunti, Chenlin Gu, Jean Christophe Mourrat

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of nongradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincaré inequalities, which are of independent interest.

Original language	English (US)
Pages (from-to)	1885-1946
Number of pages	62
Journal	Annals of Probability
Volume	50
Issue number	5
DOIs	https://doi.org/10.1214/22-AOP1573
State	Published - Sep 2022

Keywords

Hydrodynamic limit
Interacting particle system
Quantitative homogenization

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/22-AOP1573

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abstract = "For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of nongradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincar{\'e} inequalities, which are of independent interest.",

keywords = "Hydrodynamic limit, Interacting particle system, Quantitative homogenization",

author = "Arianna Giunti and Chenlin Gu and Mourrat, {Jean Christophe}",

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AU - Gu, Chenlin

AU - Mourrat, Jean Christophe

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PY - 2022/9

Y1 - 2022/9

N2 - For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of nongradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincaré inequalities, which are of independent interest.

AB - For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of nongradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincaré inequalities, which are of independent interest.

KW - Hydrodynamic limit

KW - Interacting particle system

KW - Quantitative homogenization

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JO - Annals of Probability

JF - Annals of Probability

IS - 5

ER -

QUANTITATIVE HOMOGENIZATION OF INTERACTING PARTICLE SYSTEMS

Abstract

Keywords

ASJC Scopus subject areas

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