Events for 07/17/2023 from all calendars

Workshop in Analysis and Probability Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Zhengye Zhou, Texas A&M University

Title: Orthogonal polynomial dualities of multi-species ASEP and related processes via the *-bialgebra structure of quantum groups

Abstract: In this talk, I present a general method to produce orthogonal polynomial dualities from the *–bialgebra structure of Drinfeld–Jimbo quantum groups. In the case of the quantum group 𝒰q⁢(𝔤⁢𝔩n+1), the result is a nested multivariate q–Krawtchouk duality for the n–species ASEP(q,𝜽). The method also applies to other quantized simple Lie algebras and to stochastic vertex models. As a probabilistic application of the duality relation found, we provide an explicit contour integral formula of the q−shifted factorial moments for the two–species q–TAZRP and find the asymptotics of the two–point correlations.