A product of invariant random permutations has the same small cycle structure as uniform
Combinatorics
2019-10-10 v1 Probability
Abstract
We use moment method to understand the cycle structure of the composition of independent invariant permutations. We prove that under a good control on fixed points and cycles of length 2, the limiting joint distribution of the number of small cycles is the same as in the uniform case i.e. for any positive integer k, the number of cycles of length k converges to the Poisson distribution with parameter 1/k and is asymptotically independent of the number of cycles of length k' different from k.
Keywords
Cite
@article{arxiv.1910.04031,
title = {A product of invariant random permutations has the same small cycle structure as uniform},
author = {Mohamed Slim Kammoun and Mylène Maïda},
journal= {arXiv preprint arXiv:1910.04031},
year = {2019}
}