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May, 1983 The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$
Richard Arratia
Ann. Probab. 11(2): 362-373 (May, 1983). DOI: 10.1214/aop/1176993602


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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Richard Arratia. "The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$." Ann. Probab. 11 (2) 362 - 373, May, 1983.


Published: May, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0515.60097
MathSciNet: MR690134
Digital Object Identifier: 10.1214/aop/1176993602

Primary: 60K35

Keywords: Correlation inequalities , Interacting particle system , Random permutations , simple exclusion process

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 2 • May, 1983
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