Jeffrey Kuan, Columbia University

Title: Algebraic constructions of Markov duality and its applications

Abstract: Markov duality in spin chains and exclusion processes has found a wide variety of applications throughout probability theory. We review the duality of the asymmetric simple exclusion process (ASEP) and its underlying algebraic symmetry. We then explain how the algebraic structure leads to a wide generalization of models with duality, such as higher spin exclusion processes, zero range processes, stochastic vertex models, and their multi-species analogues.

We further survey the spectral / Plancherel theory of these models, as well as its applications involving Markov duality.