Local ergodicity in the exclusion process on an infinite weighted graph

Joe P. Chen

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arXiv · 1705.10290

Local ergodicity in the exclusion process on an infinite weighted graph

Joe P. Chen

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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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Joe P. Chen. 2017-05-29. Local ergodicity in the exclusion process on an infinite weighted graph. https://arxiv.org/abs/1705.10290

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