Local ergodicity in the exclusion process on an infinite weighted graph

2017/05/29 by Joe P. Chen, Chen, Joe P.
Mathematics · Physics and Astronomy · #28A80 #31C20 #60K35 #82C22 #82C35 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1705.10290

openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1-block and 2-blocks estimates utilizing the resistance structure of the graph; the moving particle lemma established recently by the author; and discrete harmonic analysis. Our ergodic theorem applies to any infinite weighted graph upon which random walk is strongly recurrent in the sense of Barlow, Delmotte, and Telcs; these include many trees, fractal graphs, and random graphs arising from percolation. The main results of this paper are used to prove the joint density-current hydrodynamic limit of the boundary-driven exclusion process on the Sierpinski gasket, described in an upcoming paper with M. Hinz and A. Teplyaev.

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