Juggler's exclusion process describes a system of particles on the positiveintegers where particles drift down to zero at unit speed. After a particlehits zero, it jumps into a randomly chosen unoccupied site. We model the systemas a set-valued Markov process and show that the process is ergodic if thefamily of jump height distributions is uniformly integrable. In a special casewhere the particles jump according to a set-avoiding memoryless distribution,the process reaches its equilibrium in finite nonrandom time, and theequilibrium distribution can be represented as a Gibbs measure conforming to alinear gravitational potential.
"Juggler's exclusion process." J. Appl. Probab. 49 (1) 266 - 279, March 2012. https://doi.org/10.1239/jap/1331216846