Universality for random permutations and some other groups

Mohamed Slim Kammoun

Stochastic Processes and their Applications, 2022, vol. 147, issue C, 76-106

Abstract: We present a Markovian approach to prove universality results for general statistics on the symmetric group. We prove, in particular, that the number of occurrences of a vincular pattern satisfies a CLT for conjugation invariant random permutations with few cycles and we improve the results already known for the longest increasing subsequence. We give also a generalization to other random permutations and other sets having a similar structure to the symmetric group.

Date: 2022
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DOI: 10.1016/j.spa.2022.01.012

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