QUANTITATIVE HOMOGENIZATION OF INTERACTING PARTICLE SYSTEMS

• 成果类型: Article
• 署名作者: Giunti, Arianna; Gu, Chenlin; Mourrat, Jean-Christophe
• 署名单位: Imperial College London; Universite PSL; Ecole Normale Superieure (ENS); New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1573
• 发表日期: 2022
• 页码: 1885-1946
• 关键词: diffusion-coefficient matrix; finite-dimensional approximation; equilibrium fluctuations; Stochastic Homogenization; lattice-gas; REGULARITY; geometry; hydrodynamics; CONVERGENCE; EQUATIONS

摘要

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 Poincare inequalities, which are of independent interest.