Smith Colloquium

Feb 28, 2019

Leonid Petrov, University of Virginia

Title: From infinite random matrices over finite fields to square ice

Abstract: Asymptotic representation theory of symmetric groups is a rich and beautiful subject with deep connections with probability, mathematical physics, and algebraic combinatorics. A one-parameter deformation of this theory related to infinite random matrices over a finite field leads to a randomization of the classical Robinson-Schensted correspondence between words and Young tableaux. Exploring such randomizations we find unexpected applications to six vertex (square ice) type models and traffic systems on a 1-dimensional lattice.