Journal of Applied Probability

Juggler's exclusion process

Lasse Leskelä and Harri Varpanen

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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.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 266-279.

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

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


Leskelä, Lasse; Varpanen, Harri. Juggler's exclusion process. J. Appl. Probab. 49 (2012), no. 1, 266--279. doi:10.1239/jap/1331216846.

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