ASEP proofs of some partition identities and the blocking stationary behaviour of second class particles

Abstract

We give probabilistic proofs to well-known combinatorial identities; the Durfee rectangles identity, Euler’s identity and the q-Binomial Theorem. We use the asymmetric simple exclusion process on Z under its natural product blocking measure to achieve this. The results we derive also allow us to determine the stationary distribution of second class particles in the blocking scenario.

Daniel Adams

Maths and Stats Developer

My research interests include Wasserstein gradient flows, large deviations, interacting particle systems, non-equilibrium dynamics and homogenization.