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Mathematical Physics Seminar

In-Person Seminar: Eugene Speer - Approach to Hyperuniformity in Facilitated Exclusion Processes

Location:  Hill 705
Date & time: Thursday, 01 February 2024 at 12:00PM - 1:00PM

Eugene Speer – Rutgers University

February 1st, 12:00pm; Hill Center 705

Approach to Hyperuniformity in Facilitated Exclusion Processes


A (probabilistic) translation invariant state of a system of particles on a lattice is called hyperuniform if the variance of the number of particles in a box grows more slowly than the volume of the box. Such states arise as infinite-time limits, at a critical particle density, of states of Facilitated Exclusion Processes---processes in which particles on the lattice can jump to neighboring empty sites if facilitated by an occupied neighboring site.  Simulations of these systems in dimension two and higher also show an interesting approach to hyperuniformity as the density approaches the critical value from below.  In this talk we will describe these phenomena in more detail and sketch a proof of the corresponding results in one dimension; the proof involves the study of renewal processes with long tails.

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