Vadim Gorin ; Greta Panova - Asymptotics of symmetric polynomials

dmtcs:12791 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12791
Asymptotics of symmetric polynomialsArticle

Authors: Vadim Gorin 1,2; Greta Panova 3

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Schur functions,asymptotics,GUE,ASM,infinite-dimensional unitary group,dense loop model,lozenge tilings,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

Consultation statistics

This page has been seen 55 times.
This article's PDF has been downloaded 46 times.