Duality in integrable stochastic systems
by Michael Wheeler
Abstract: Given two independent Markov processes with configuration spaces X and Y, a duality function is an observable valued on X \times Y whose expected value in one process is equal to its expected value in the other. Such stochastic dualities can be an important computational tool, especially when one of the Markov processes is easier to analyse than its dual counterpart.
This talk will provide a general introduction to these dualities, focusing on the particular example in which both systems are asymmetric simple exclusion processes (ASEPs). I will explain some recently developed techniques which enable the construction of rich classes of duality functions within the ASEP. These techniques draw from the theory of quantized affine algebras, the quantum Knizhnik--Zamolodchikov equation, and integrable lattice models.
This is based on joint work with Zeying Chen and Jan de Gier.