Local ergodicity in the exclusion process on an infinite weighted graph
Abstract
We establish an abstract local ergodic theorem, under suitable spacetime scaling, for the (boundarydriven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1block and 2blocks 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 densitycurrent hydrodynamic limit of the boundarydriven exclusion process on the Sierpinski gasket, described in an upcoming paper with M. Hinz and A. Teplyaev.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 arXiv:
 arXiv:1705.10290
 Bibcode:
 2017arXiv170510290C
 Keywords:

 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 28A80;
 31C20;
 60K35;
 82C22;
 82C35
 EPrint:
 v2: 36 pages, 5 figures. Minor typos corrected