%0 Journal Article
%T Juggler's exclusion process
%A Lasse Leskel£¿
%A Harri Varpanen
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1104.3397v2