Quantitative homogenization of interacting particle systems. (English) Zbl 1500.35021

Giunti, Arianna; Gu, Chenlin; Mourrat, Jean-Christophe

Ann. Probab. 50, No. 5, 1885-1946 (2022).

Summary: 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.

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
60K35	Interacting random processes; statistical mechanics type models; percolation theory
82C22	Interacting particle systems in time-dependent statistical mechanics

Keywords:

hydrodynamic limit; interacting particle system; quantitative homogenization

References:

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