10/06/2026, 17:00 — 18:00 Europe/Lisbon —
Online
Michael Conroy, Clemson University
Poisson limits in nonequilibrium generalized symmetric exclusion systems
The generalized exclusion system on Z models the dynamics of particles with strong local interaction induced by an exclusion rule in which at most K particles may occupy the same site. When the underlying random walks have symmetric transition rates and particle locations are initialized according to a (possibly non-homogeneous) product Binomial measure, the occupation variables of the system obey a strong form of negative association called the strong Rayleigh property. As shown by Liggett (2009), this property yields simply-stated (but abstract) conditions for the scaled number of particles in a set to converge to a Poisson distribution. This extends naturally to conditions for convergence of the point process of particle positions to a Poisson random measure (PRM) on the real line. A precise analysis of particle covariances gives explicit scaling limits to a PRM with exponential intensity in the context of translation invariance and a highly-nonequilibrium `step’ initial condition in which infinitely many particles lie below a maximal one. Moreover, these limit theorems can be extended to certain initial conditions outside the strong-Rayleigh context. This talk will discuss joint work with Adrian Gonzalez Casanova (Arizona State) and Sunder Sethuraman (Arizona).
Senha de Zoom: 359751
