Asymptotics of characters of symmetric groups, genus expansion and free probability.

DOI10.1016/j.disc.2006.02.004zbMath1096.20016arXivmath/0411647OpenAlexW2135217831MaRDI QIDQ2488939

Piotr Śniady

Publication date: 16 May 2006

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411647

zbMATH Keywords

group algebrassymmetric groupscharactersasymptotic expansionsGaussian unitary ensemblefree probabilityYoung diagramsJucys-Murphy elementstransition measures

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items

Gaussian fluctuations of Young diagrams and structure constants of Jack characters ⋮ Combinatorial interpretation and positivity of Kerov's character polynomials ⋮ Shifted symmetric functions and multirectangular coordinates of Young diagrams ⋮ Positivity results for Stanley's character polynomials ⋮ Stanley's character polynomials and coloured factorisations in the symmetric group ⋮ Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula. ⋮ Asymptotics of characters of symmetric groups: structure of Kerov character polynomials ⋮ Quadratic coefficients of Goulden-Rattan character polynomials ⋮ Quantum spectrum testing ⋮ Two positivity conjectures for Kerov polynomials ⋮ Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations ⋮ Gaussian fluctuations of characters of symmetric groups and of Young diagrams ⋮ Jack polynomials and free cumulants ⋮ GAUSSIAN FLUCTUATIONS OF REPRESENTATIONS OF WREATH PRODUCTS ⋮ Jeu de taquin dynamics on infinite Young tableaux and second class particles ⋮ An explicit form for Kerov's character polynomials

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