# Local ergodicity in the exclusion process on an infinite weighted graph

@article{Chen2017LocalEI, title={Local ergodicity in the exclusion process on an infinite weighted graph}, author={Joe P. J. Chen}, journal={arXiv: Probability}, year={2017} }

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… Expand

#### 2 Citations

The moving particle lemma for the exclusion process on a weighted graph

- Mathematics, Physics
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We prove a version of the moving particle lemma for the exclusion process on any finite weighted graph, based on the octopus inequality of Caputo, Liggett, and Richthammer. In light of their proof of… Expand

From non-symmetric particle systems to non-linear PDEs on fractals

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We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging to a non-linear… Expand

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