QUANTITATIVE HOMOGENIZATION OF INTERACTING PARTICLE SYSTEMS

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.

Automated summary

This study demonstrates the algebraic convergence of finite-volume approximations of the bulk diffusion matrix for interacting particle systems in continuous space. The models considered are reversible with respect to Poisson measures of constant density and are of nongradient type. The study also introduces modified Caccioppoli and multiscale Poincare inequalities of independent interest.