Approximate factorization and concentration for characters of symmetric groups

2000/06/15 by Philippe Biane, Biane, Philippe · 4 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #math.PR #math.RT

paper · pdf · doi:10.48550/arxiv.math/0006111

12 pages, 2 figures

openalex publication_date 2000/06/15 · arxiv created 2000/06/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a factorization-concentration result for characters of symmetric groups. This is then applied to the asymptotic behaviour of the decomposition of the tensor representations. There are connections with the Pastur-Marcenko distribution of random matrix theory, and freely infinitely divisible distributions.

Cited by

• Random Young diagrams and Jacobi Unitary Ensemble
• Time evolution of averaged limit shapes of random multiple Young diagrams
• Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions
• Kerov's central limit theorem for Schur-Weyl measures of parameter 1/2

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• Central Limit Theorem on the Conjugacy Measure of Symmetric Groups
• Partial sum of matrix entries of representations of the symmetric group and its asymptotics
• A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra
• Stein's Method and Plancherel Measure of the Symmetric Group