Asymptotic normality of pattern counts in conjugacy classes

2023/12/14 by Valentin Féray, Féray, Valentin, Mohamed Slim Kammoun +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Stochastic processes and statistical mechanics #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2312.08756

Abstract

We prove, under mild conditions on fixed points and two cycles, the asymptotic normality of vincular pattern counts for a permutation chosen uniformly at random in a conjugacy class.Additionally, we prove that the limiting variance is always non-degenerate for classical pattern counts. The proof uses weighted dependency graphs.

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