From infinite random matrices over finite fields to square ice


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.

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A simulation of the square ice, due to Shreyas Balaji (MIT UROP)
A simulation of the square ice, due to Shreyas Balaji (MIT UROP)