Arvind Ayyer: Combinatorial connections to yet another statistical mechanical model

Abstract

I will define a Markov chain called an asymmetric annihilation process (AAP) on a finite one dimensional lattice where each site is either occupied or empty. The dynamics is then defined by (1) totally asymmetric exclusion and (2) pairwise annihilation. The aim is to understand the stationary distribution in terms of tilings of aztec diamonds, just as the stationary distribution of the asymmetric exclusion process was understood in terms of permutation tableaux. I will establish some links towards this program. In a different direction, all the eigenvalues of the transition matrix of the Markov chain have degeneracies which are binomial coefficients. Yet another aspect of this model links it to a new weight on strict partitions with connections to symmetric functions with many sets of variables. This is based on joint works with Kirone Mallick, Volker Strehl and Alain Lascoux.