2013

Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory

Gorin, Vadim, Panova, Greta

Understand

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity.

Several applications of our method are presented: We prove a number of theorems concerning characters of infinite-dimensional unitary group and their $q$-deformations.
We study the behavior of uniformly random lozenge tilings of large polygonal domains and find the GUE-eigenvalues distribution in the limit.
We also investigate similar behavior for alternating sign matrices (equivalently, six-vertex model with domain wall boundary conditions).

Built on

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