Representation Theory and Mathematical Physics Seminar: Algebraic constructions of Markov duality functions

Seminar | November 8 | 4-5 p.m. | 939 Evans Hall

 Jeffrey Kuan, Columbia University

 Department of Mathematics

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: in particular, there is an underlying quantum group and affine Lie algebra 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.