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Juggler’s exclusion process. (English) Zbl 1242.60103
The present paper deals with the following problem. 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. The authors 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 the 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
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