A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra

2011/04/30 by Pierre‐Loïc Méliot, Pierre-Loïc Méliot, Méliot, Pierre-Loïc · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #FOS: Mathematics #Random Matrices and Applications #Representation Theory (math.RT) #Stochastic processes and statistical mechanics #math.RT

paper · pdf · doi:10.48550/arxiv.1105.0091

70 pages, 9 figures

arxiv created 2011/04/30 · openalex publication_date 2011/04/30 · arxiv updated 2011/05/03 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

In this paper, we review the representation theory of the infinite symmetric group, and we extend the works of Kerov and Vershik by proving that the irreducible characters of the infinite symmetric group always satisfy a central limit theorem. Hence, for any point of the Thoma simplex, the corresponding measures on the levels of the Young graph have a property of gaussian concentration. By using the Robinson-Schensted-Knuth algorithm and the theory of Pitman operators, we relate these results to the properties of certain random permutations obtained by riffle shuffles, and to the behaviour of random walks conditioned to stay in a Weyl chamber.

Citations

• Gaussian concentration of the q-characters of the Hecke algebras of type A

Cited by

• The central limit theorem for extremal characters of the infinite symmetric group

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