March 2012 Juggler's exclusion process
Lasse Leskelä, Harri Varpanen
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J. Appl. Probab. 49(1): 266-279 (March 2012). DOI: 10.1239/jap/1331216846

Abstract

Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.

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Lasse Leskelä. Harri Varpanen. "Juggler's exclusion process." J. Appl. Probab. 49 (1) 266 - 279, March 2012. https://doi.org/10.1239/jap/1331216846

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

MathSciNet: MR2952894
zbMATH: 1242.60103
Digital Object Identifier: 10.1239/jap/1331216846

Subjects:
Primary: 60K35
Secondary: 82C41

Keywords: ergodicity , Exclusion process , Gibbs measure , juggling pattern , maximum entropy , noncolliding random walk , positive recurrence , set-avoiding memoryless distribution , set-valued Markov process

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 1 • March 2012
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