Asymptotic normality of pattern counts in conjugacy classes

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.

Bayesian Methods and Mixture Models Stochastic processes and statistical mechanics Analytic Number Theory Research

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