Vadim Gorin, Greta Panova
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.
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http://arxiv.org/abs/1301.0634
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