Quantitative homogenization of interacting particle systems
Probability
2021-12-07 v2 Analysis of PDEs
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 non-gradient 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.
Cite
@article{arxiv.2011.06366,
title = {Quantitative homogenization of interacting particle systems},
author = {Arianna Giunti and Chenlin Gu and Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:2011.06366},
year = {2021}
}
Comments
60 pages, 6 figures; a new section is added to the appendix