  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.
