Event Type:

Department Colloquium

Date/Time:

Monday, November 15, 2021 - 16:00 to 17:00

Location:

KEAR 112

Guest Speaker:

Institution:

University of Virginia and MSRI

Abstract:

I will survey results on stochastic interacting particle systems (such as TASEP, the Totally Asymmetric Simple Exclusion Process) in the presence of inhomogeneity. That is, we consider particles with variable speeds, so that the environment of the particles contains "swamps and highways", where particles move with variable speed. This inserts multiple parameters into the system, but in some miraculous cases the system stays exactly solvable in the presence of the parameters. This allows one to prove interesting asymptotic phase transitions. Moreover, permutations of the multiple parameters can sometimes be realized as Markov operators on the state of the system, which leads to intriguing structural properties.

Host: