Cycle structure of random standardized permutations

Date/heure
29 avril 2026
16:45 - 17:45

Oratrice ou orateur
Aurélien Guerder

Catégorie d'évènement
Séminaire des doctorants


Résumé

We study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. discrete random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased permutations. We first establish an exact result on the joint distribution of the number of cycles of given lengths, involving the notion of primitive words. Thanks to this result obtained via combinatorial methods, we obtain convergence in distribution as the size of the permutation tends to infinity . This talk will be an opportunity to introduce (or recall) the method of moments, a very useful tool for proving convergence in distribution, particularly for combinatorial objects. We will present a few limit results on the distribution of « small » and « large » cycles of the permutation, as well as on the total number of cycles.