Universality for random permutations and some other groups
Probability
2020-12-11 v1 Combinatorics
Abstract
We present some Markovian approaches to prove universality results for some functions on the symmetric group. Some of those statistics are already studied in [Kammoun, 2018, 2020] but not the general case. We prove, in particular, that the number of occurrences of a vincular patterns satisfies a CLT for conjugation invariant random permutations with few cycles and we improve the results already known for the longest increasing subsequence. The second approach is a suggestion of a generalization to other random permutations and other sets having a similar structure than the symmetric group.
Cite
@article{arxiv.2012.05845,
title = {Universality for random permutations and some other groups},
author = {Mohamed Slim Kammoun},
journal= {arXiv preprint arXiv:2012.05845},
year = {2020}
}