The Annals of Probability

The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$

Richard Arratia

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Consider a system of particles moving on the integers with a simple exclusion interaction: each particle independently attempts to execute a simple symmetric random walk, but any jump which would carry a particle to an already occupied site is suppressed. For the system running in equilibrium, we analyze the motion of a tagged particle. This solves a problem posed in Spitzer's 1970 paper "Interaction of Markov Processes." The analogous question for systems which are not one-dimensional, nearest-neighbor, and either symmetric or one-sided remains open. A key tool is Harris's theorem on positive correlations in attractive Markov processes. Results are also obtained for the rightmost particle in the exclusion system with initial configuration $Z^-$, and for comparison systems based on the order statistics of independent motions on the line.

Article information

Ann. Probab., Volume 11, Number 2 (1983), 362-373.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Interacting particle system simple exclusion process random permutations correlation inequalities


Arratia, Richard. The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$. Ann. Probab. 11 (1983), no. 2, 362--373. doi:10.1214/aop/1176993602.

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