Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory
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1301.0634.pdf
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Author(s)
Gorin, Vadim
Panova, Greta
Date Issued
July 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/14-AOP955
