English

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].

Keywords

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

R2 v1 2026-06-22T14:18:14.451Z