Orateur
Slim Kammoun
Description
We are interested in the cycle structure of words in several random permutations.
The first part of the talk will be dedicated to recall classic results (Nica 1994) when the permutations are i.i.d uniform of size n.
In the second part, we assume that the permutations are independent and that their distribution is conjugacy invariant, with a good control on their short cycles. If, after successive cyclic simplifications, the word w still contains at least two different letters, then we get a universal limiting joint law for small cycles for the word in these permutations.
The third part will be dedicated to the discussion of some open problems.
This talk is based on a joint work with Mylène Maïda (ArXiv 2204.04759).
