Juggler's exclusion process

Details Juggler's exclusion process Juggler's exclusion process

2011-04-18

arxiv.org/abs/1104.3397v1

Mathematics

Probability

17 pages, 1 figure

Scientific paper

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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