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

Author(s)
Gorin, Vadim; Panova, Greta
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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.
Date issued
2014-07
URI
http://hdl.handle.net/1721.1/116157
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Citation
Gorin, Vadim, and Greta Panova. “Asymptotics of Symmetric Polynomials with Applications to Statistical Mechanics and Representation Theory.” The Annals of Probability 43, 6 (November 2015): 3052–3132 © 2015 Institute of Mathematical Statistics
Version: Final published version
ISSN
0091-1798

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