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2019 Mixing times for exclusion processes on hypergraphs
Stephen B. Connor, Richard J. Pymar
Electron. J. Probab. 24: 1-48 (2019). DOI: 10.1214/19-EJP332


We introduce a natural extension of the exclusion process to hypergraphs and prove an upper bound for its mixing time. In particular we show the existence of a constant $C$ such that for any connected, regular hypergraph $G$ within some natural class, the $\varepsilon $-mixing time of the exclusion process on $G$ with any feasible number of particles can be upper-bounded by $CT_{\text{EX} (2,G)}\log (|V|/\varepsilon )$, where $|V|$ is the number of vertices in $G$ and $T_{\text{EX} (2,G)}$ is the 1/4-mixing time of the corresponding exclusion process with just two particles. Moreover we show this is optimal in the sense that there exist hypergraphs in the same class for which $T_{\mathrm{EX} (2,G)}$ and the mixing time of just one particle are not comparable. The proofs involve an adaptation of the chameleon process, a technical tool invented by Morris ([14]) and developed by Oliveira ([15]) for studying the exclusion process on a graph.


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Stephen B. Connor. Richard J. Pymar. "Mixing times for exclusion processes on hypergraphs." Electron. J. Probab. 24 1 - 48, 2019.


Received: 23 March 2018; Accepted: 9 June 2019; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07089011
MathSciNet: MR3978223
Digital Object Identifier: 10.1214/19-EJP332

Primary: 60J27 , 60K35
Secondary: 82C22

Keywords: coupling , exclusion , Hypergraph , interchange , mixing time , Random walk


Vol.24 • 2019
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