@article{cdf628abd5644eb88183063e349d1bae,

title = "QUANTITATIVE HOMOGENIZATION OF INTERACTING PARTICLE SYSTEMS",

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 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 Poincar{\'e} inequalities, which are of independent interest.",

keywords = "Hydrodynamic limit, Interacting particle system, Quantitative homogenization",

author = "Arianna Giunti and Chenlin Gu and Mourrat, {Jean Christophe}",

note = "Funding Information: where we used the quadratic response (69) from the second line to the third line. This implies that limm→∞(141)-b1 = 0, and thus completes the proof of (128). □ Funding. 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). Funding Information: 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). Funding Information: 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. Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2022",

year = "2022",

month = sep,

doi = "10.1214/22-AOP1573",

language = "English (US)",

volume = "50",

pages = "1885--1946",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "5",

}