Agenda de l’IDP

Séminaire SPACE Tours

Random walks in braid groups converge
Vincent Jugé (LIAFA)
Friday 13 May 2016 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
Consider a finitely generated group with an associated notion of normal form, and consider a random walk on the group. Does the normal form of the random elements converge? In 2000, A. Vershik asked this question for the case of braid groups and conjectured that the answer should be positive for a wide class of normal forms, such as the Garside normal form or Birman-Ko-Lee normal form. In 2007, together with A. Malyutin, he provided a positive answer for the braid groups with the Markov-Ivanovsky normal form. In this presentation, we answer the question by the affirmative for irreducible Artin-Tits groups of spherical type with the Garside normal form. We will first investigate the already well-known case of trace monoids and groups, then show how we can twist our proof to derive analogous results in the case of braid monoids and groups, and even obtain some insight on the behaviour of the limit of these random walks. This is a work in progress, in collaboration with Jean Mairesse.

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