The Annals of Probability

Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk

Roberto Imbuzeiro Oliveira

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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.

Article information

Source
Ann. Probab., Volume 41, Number 2 (2013), 871-913.

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1362750945

Digital Object Identifier
doi:10.1214/11-AOP714

Mathematical Reviews number (MathSciNet)
MR3077529

Zentralblatt MATH identifier
1274.60242

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Symmetric exclusion interchange process mixing time

Citation

Oliveira, Roberto Imbuzeiro. Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk. Ann. Probab. 41 (2013), no. 2, 871--913. doi:10.1214/11-AOP714. https://projecteuclid.org/euclid.aop/1362750945


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