Electronic Communications in Probability

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

Joe P. Chen

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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].

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 47, 13 pp.

Dates
Received: 3 June 2016
Accepted: 29 August 2017
First available in Project Euclid: 2 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1506931447

Digital Object Identifier
doi:10.1214/17-ECP82

Mathematical Reviews number (MathSciNet)
MR3710803

Zentralblatt MATH identifier
1372.05207

Subjects
Primary: 05C81: Random walks on graphs 28A80: Fractals [See also 37Fxx] 31C20: Discrete potential theory and numerical methods 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]

Keywords
exclusion process moving particle lemma interchange process electric network effective resistance

Rights
Creative Commons Attribution 4.0 International License.

Citation

Chen, Joe P. The moving particle lemma for the exclusion process on a weighted graph. Electron. Commun. Probab. 22 (2017), paper no. 47, 13 pp. doi:10.1214/17-ECP82. https://projecteuclid.org/euclid.ecp/1506931447


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References

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