11/10/2023, 17:00 — 18:00 — Online
Michael Conroy, University of Arizona
Extreme values in the symmetric exclusion process
In the one-dimensional exclusion system, a step initial condition is one with infinitely many particles to the left and none to the right of a maximal one. Assuming symmetric, nearest-neighbor interaction, if we tag the right-most particle and follow its (properly scaled) position as time grows, we see a Gumbel limit distribution. Interestingly, this matches the behavior of the maximum of independent particles started from the same initial profile, as studied by Arratia (1983). Unlike with independent particles, proving the result for the exclusion process requires a careful analysis of pair-wise correlations, which rests on duality and negative association properties of symmetric exclusion. Limiting Gumbel distributions can also be obtained in higher dimensions by considering initial conditions where infinitely many particles occupy points in a half-space. This talk is based on joint work with Sunder Sethuraman.
