Atypical behaviors of a tagged particle in asymmetric simple exclusion
Mathematical Physics and Probability Seminar
Atypical behaviors of a tagged particle in asymmetric simple exclusion
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Sunder Sethuraman, University of Arizona
Informally, the one dimensional asymmetric simple exclusion process follows a collection of continuous time random walks on Z interacting as follows: When a clock rings, the particle jumps to the nearest right or left with probabilities p or q=1-p, if that location is unoccupied. If occupied, the jump is suppressed and clocks start again.
In such a system, the motion of a distinguished or `tagged' particle is of interest. Starting from a stationary state, we study the `typical' behavior of a tagged particle, conditioned to deviate to an `atypical' position at a fixed time. In the course of results, an `upper tail' large deviation principle is established for the position of the tagged particle. Also, with respect to `lower tail' events, in the totally asymmetric version, a connection is made with a `nonentropy' solution of the associated hydrodynamic Burgers equation. This is work with S.R.S. Varadhan (arXiv:2311.0780).
(zoom: https://arizona.zoom.us/j/86800353711)