Juggler's exclusion process

TL;DR

The paper introduces the Juggler's exclusion process, modeling particles on positive integers with specific jump dynamics, and analyzes its ergodic behavior and equilibrium properties.

Contribution

It models the process as a set-valued Markov process and characterizes conditions for ergodicity and explicit equilibrium distributions.

Findings

Process is ergodic under uniform integrability of jump distributions.

In a special case, the process reaches equilibrium in finite nonrandom time.

Equilibrium distribution can be expressed as a Gibbs measure.

Abstract

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.