The Annals of Probability

Symmetric Exclusion Processes: A Comparison Inequality and a Large Deviation Result

Richard Arratia

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Abstract

We consider an infinite particle system, the simple exclusion process, which was introduced in the 1970 paper "Interaction of Markov Processes," by Spitzer. In this system, particles attempt to move independently according to a Markov kernel on a countable set of sites, but any jump which would take a particle to an already occupied site is suppressed. In the case that the Markov kernel is symmetric, an inequality by Liggett gives a comparison, for expectations of positive definite functions, between the exclusion process and a system of independent particles. We apply a special case of this inequality to an auxiliary process, to prove another comparison inequality, and to derive a large deviation result for the symmetric exclusion system. In the special case of simple random walks on $Z$, this result can be transformed into a large deviation result for an infinite network of queues.

Article information

Source
Ann. Probab., Volume 13, Number 1 (1985), 53-61.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993065

Digital Object Identifier
doi:10.1214/aop/1176993065

Mathematical Reviews number (MathSciNet)
MR770627

Zentralblatt MATH identifier
0558.60075

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F10: Large deviations 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Interacting particle system exclusion process large deviations Jackson networks random stirrings random transpositions random shuffling

Citation

Arratia, Richard. Symmetric Exclusion Processes: A Comparison Inequality and a Large Deviation Result. Ann. Probab. 13 (1985), no. 1, 53--61. doi:10.1214/aop/1176993065. https://projecteuclid.org/euclid.aop/1176993065


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