Séminaire de Mathématique

A Glimpse of Random Walks on (Quantum?!) Groups

by Amaury Freslon (Paris-Saclay & IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Probability and analysis informal seminar

Random walks on groups are nice examples of Markov chains which arise quite naturally in many situations. Their key feature is that one can use the algebraic properties of the group to gain a fine understanding of the asymptotic behaviour. For instance, it has been observed that some random walks exhibit a very sharp phase transition called the cut-off phenomenon. I will first explain this phenomenon on a concrete example, introducing all the necessary material. Then, I will give some ideas on how the setting may be enlarged to encompass more general stochastic processes (called non-commutative Markov chains) by using a strange algebraic structure called a quantum group.



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Organized by

Thierry Bodineau, Pieter Lammers, Yilin Wang