The moving particle lemma for the exclusion process on a weighted graph
Probability
2017-10-03 v4 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
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 Aldous' spectral gap conjecture, we conjecture that our moving particle lemma is optimal in general. Our result can be applied to graphs which lack translational invariance, including, but not limited to, fractal graphs. An application of our result is the proof of local ergodicity for the exclusion process on a class of weighted graphs, the details of which are reported in a follow-up paper [arXiv:1705.10290].
Cite
@article{arxiv.1606.01577,
title = {The moving particle lemma for the exclusion process on a weighted graph},
author = {Joe P. Chen},
journal= {arXiv preprint arXiv:1606.01577},
year = {2017}
}
Comments
v4: 10 pages, 1 figure. Small typos corrected