Fine structure of moments of the KMK transform of the Poissonized Plancharel measure

2016/07/20 by Patrick Waters, Waters, Patrick
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #math.CO #math.PR

paper · pdf · doi:10.48550/arxiv.1607.06150

openalex publication_date 2016/07/20 · arxiv created 2016/08/21 · arxiv updated 2016/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider asymptotics behavior of Poissonized Plancharel measures as the poissonization parameter N goes to infinity. Recently Moll proved a convergent series expansion for statistics of a measure μ_λ which is the Kerov-Markov-Krein transform of the signed measure on corners a Jack-random partition λ. The measure μ_λ is of interest because it behaves in some ways like the empirical measure on eigenvalues of a GUE-random matrix. We prove for the Poissonized Plancharel case that the large N series for moments of μ_λ have a recursive structure as rational expressions in the generating function for Catalan numbers. We discuss the analogy between our result and the fine structure of moments of the GUE.

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