Probability and Mathematical Physics Seminar

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Fluctuations in weakly asymmetric simple exclusion process on a ring subject to an atypical current

Speaker: Benoit Dagallier, Courant Institute

Location: Warren Weaver Hall 1302

Date: Friday, September 15, 2023, 11:10 a.m.

Synopsis:

The broad aim of the talk is to describe the dynamics of interacting particle systems on rare dynamical events. For many models large deviation results are available and give an estimate of the probability of such a rare event. The point here is to describe the trajectories belonging to this rare event, in the high-dimensional limit where the number of particles is large.

From a technical point of view, the difficulty is that the original dynamics "conditioned" (in a suitable sense) to the rare dynamical event is high-dimensional, in general non-local (even if the original dynamics were local), non homogeneous in time and not explicitly known. The study of such dynamics on rare events is of particular interest when the interacting particle system undergoes a dynamical phase transition.

I will consider a simple yet already very rich model: the Weakly Asymmetric Simple Exclusion Process (WASEP) on a ring, subject to an atypical current of particles. The WASEP has a dynamical phase transition when the current strength exceeds a certain threshold. Using so-called relative entropy techniques, it is possible to obtain a detailed description of the WASEP dynamics tilted by the current. In particular I can compute spatial (two-point) correlations, confirming 2007 heuristic computations of Thierry Bodineau and Bernard Derrida and giving information on the dynamical phase transition.