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

Richard Arratia
The Annals of Probability
Vol. 11, No. 2 (May, 1983), pp. 362-373
Stable URL: http://www.jstor.org/stable/2243693
Page Count: 12
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The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on Z
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Abstract

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.

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