Abstract
We prove, under mild conditions on fixed points and 2-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.
Funding Statement
Mohamed Slim Kammoun is supported by ERC Project LDRAM: ERC-2019-ADG Project 884584. Valentin Féray is partially supported by a Future Leader grant from the initiative Lorraine Université d’Excellence (LUE).
Acknowledgments
Both authors want to thank Zachary Hamaker and Victor Dubach for insightful discussions and an anonymous referee for their careful reading of the article and their insightful comments.
Citation
Valentin Féray. Mohamed Slim Kammoun. "Asymptotic normality of pattern counts in conjugacy classes." Electron. J. Probab. 29 1 - 22, 2024. https://doi.org/10.1214/24-EJP1113
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