Juggler's Exclusion Process
Speaker:\n\nProf. L. Leskela\u0308\n\n\nAbstract:\n\nJuggler'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. I will 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 perform jumps according to an entropy-maximizing fashion, 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. Time permitting, I will also discuss a recent result which sharply characterizes uniform integrability using the theory of stochastic orders, and allows to interpret the dominating function in Lebesgue's dominated convergence theorem in a natural probabilistic way.\r\rThis talk is based on joint work with Harri Varpanen (Aalto University, Finland) and Matti Vihola (University of Jyva\u0308skyla\u0308, Finland).