Variance of Linear Statistic for Plancherel Young Diagrams

2012/02/08 by Konstantin Tolmachov, Tolmachov, Konstantin
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #Stochastic processes and statistical mechanics #math.PR #math.RT

paper · pdf · doi:10.48550/arxiv.1202.1806

arxiv created 2012/02/08 · openalex publication_date 2012/02/08 · arxiv updated 2012/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we compute the precise asymptotics of the variance of linear statistic of descents on a growing interval for Plancherel Young diagrams (following Vershik and Kerov, diagrams are considered rotated by π/4). We also give an example of a local configuration with linearly growing variance in a fixed regime and prove the central limit theorem for this configuration in the given regime.

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• On Descents in Standard Young Tableaux