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.
Part of this project was developed while AG was affiliated to the University of Bonn and supported through the CRC 1060 (The Mathematics of Emergent Effects) that is funded through the German Science Foundation (DFG), and the Hausdorff Center for Mathematics (HCM).
CG was supported by a Ph.D. scholarship from Ecole Polytechnique. Part of this project was developed while CG was an academic visitor at the Courant Institute, NYU.
JCM was partially supported by NSF Grant DMS-1954357. Part of this project was developed while JCM was affiliated with CNRS and ENS Paris, PSL University, and was partially supported by the ANR Grants LSD (ANR-15-CE40-0020-03) and Malin (ANR-16-CE93-0003).
"Quantitative homogenization of interacting particle systems." Ann. Probab. 50 (5) 1885 - 1946, September 2022. https://doi.org/10.1214/22-AOP1573