# Asymptotics of symmetric polynomials

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 the $O(n=1)$ dense loop model.
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Conference papers

https://hal.inria.fr/hal-01229718
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Submitted on : Tuesday, November 17, 2015 - 10:20:31 AM
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• HAL Id : hal-01229718, version 1

### Citation

Vadim Gorin, Greta Panova. Asymptotics of symmetric polynomials. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.37-48. ⟨hal-01229718⟩

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