Brown University School of Engineering

Applied Mathematics Colloquium presents Lauren K. Williams, Harvard University

Tuesday, December 11, 2018

12:00pm - 1:00pm

Applied Mathematics

170 Hope Street, 108

Introduction to the asymmetric simple exclusion process (from a combinatorialist’s point of view)  

Lauren K. Williams
Harvard, Department of Mathematics

The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, subject to the condition that there is at most one particle per site.  This model was introduced in 1970 by biologists (as a model for translation in protein synthesis) but has since been shown to display a rich mathematical structure.  There are many variants of the model – e.g. the lattice could be a ring, or a line with open boundaries.  One can also allow multiple species of particles with different “weights.”  I will explain how one can give combinatorial formulas for the stationary distribution using various kinds of tableaux.  I will also explain how the ASEP is related to interesting families of orthogonal polynomials, including Askey-Wilson polynomials, Koornwinder polynomials, and Macdonald polynomials.  Based on joint work with Sylvie Corteel (Paris) and Olya Mandelshtam (Brown).