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March 2013 Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
Roberto Imbuzeiro Oliveira
Ann. Probab. 41(2): 871-913 (March 2013). DOI: 10.1214/11-AOP714

Abstract

We prove an upper bound for the $\varepsilon$-mixing time of the symmetric exclusion process on any graph $G$, with any feasible number of particles. Our estimate is proportional to ${\mathsf{T}}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon )$, where $|V|$ is the number of vertices in $G$, and ${\mathsf{T}}_{\mathsf{RW}(G)}$ is the $1/4$-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdös–Rényi random graph and Poisson point processes in $\mathbb{R}^{d}$. Our technical tools include a variant of Morris’s chameleon process.

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Roberto Imbuzeiro Oliveira. "Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk." Ann. Probab. 41 (2) 871 - 913, March 2013. https://doi.org/10.1214/11-AOP714

Information

Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1274.60242
MathSciNet: MR3077529
Digital Object Identifier: 10.1214/11-AOP714

Subjects:
Primary: 60J27, 60K35
Secondary: 82C22

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • March 2013
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