Journal of Applied Probability
- J. Appl. Probab.
- Volume 49, Number 1 (2012), 266-279.
Juggler's exclusion process
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.
J. Appl. Probab., Volume 49, Number 1 (2012), 266-279.
First available in Project Euclid: 8 March 2012
Permanent link to this document
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]
Leskelä, Lasse; Varpanen, Harri. Juggler's exclusion process. J. Appl. Probab. 49 (2012), no. 1, 266--279. doi:10.1239/jap/1331216846. https://projecteuclid.org/euclid.jap/1331216846