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Juggler's Exclusion Process

Part of: Special processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  04 February 2016

Lasse Leskelä  and
Harri Varpanen
Lasse Leskelä*
Affiliation:
University of Jyväskylä
Harri Varpanen*
Affiliation:
Aalto University
*
∗ Postal address: Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35, 40014, Finland. Email address: lasse.leskela@iki.fi
∗∗ Postal address: Department of Mathematics and Systems Analysis, Aalto University, PO Box 11100, 00076 Aalto, Finland. Email address: harri.varpanen@tkk.fi
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Abstract

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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.

Keywords

Exclusion processjuggling patternset-valued Markov processergodicitypositive recurrenceset-avoiding memoryless distributionnoncolliding random walkGibbs measuremaximum entropy

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc.
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 266 - 279
Copyright
© Applied Probability Trust 

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