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November 2015 Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory
Vadim Gorin, Greta Panova
Ann. Probab. 43(6): 3052-3132 (November 2015). DOI: 10.1214/14-AOP955

Abstract

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). Finally, we compute the asymptotic expansion of certain observables in $O(n=1)$ dense loop model.

Citation

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Vadim Gorin. Greta Panova. "Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory." Ann. Probab. 43 (6) 3052 - 3132, November 2015. https://doi.org/10.1214/14-AOP955

Information

Received: 1 July 2013; Revised: 1 July 2014; Published: November 2015
First available in Project Euclid: 11 December 2015

zbMATH: 06541353
MathSciNet: MR3433577
Digital Object Identifier: 10.1214/14-AOP955

Subjects:
Primary: 05E05, 22E99, 60F99, 60K35

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 6 • November 2015
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