Asymptotic normality of pattern counts in conjugacy classes
Combinatorics
2024-03-12 v2 Probability
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.
Cite
@article{arxiv.2312.08756,
title = {Asymptotic normality of pattern counts in conjugacy classes},
author = {Valentin Féray and Mohamed Slim Kammoun},
journal= {arXiv preprint arXiv:2312.08756},
year = {2024}
}