The Eigenvalue Point Process for Symmetric Group Permutation\n Representations on k-tuples

2019/01/20 by Benjamin K. Tsou, Tsou, Benjamin
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Diffusion and Search Dynamics #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1901.06721

openalex publication_date 2019/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Equip the symmetric group mathfrakS_n with the Ewens distribution. We\nstudy the eigenvalue point process of the permutation representation of\n mathfrakS_n on k-tuples of distinct integers chosen from the set\n 1,2,...,n . Taking n \→ \∞, we find the limiting point process in\nthe microscopic regime, i.e. when the eigenvalue point process is viewed at the\nscale of the mean eigenvalue spacing. A formula for the limiting eigenvalue gap\nprobability in an interval is also given. In certain cases, a power series\nrepresentation exists and a combinatorial procedure is given for computing the\ncoefficients.\n

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