An entropic criterion for cutoff

Justin Salez, Université Paris-Dauphine & PSL
Fine Hall 214

In-Person Talk 

Discovered by Aldous, Diaconis and Shahshahani in the context of card shuffling, the cutoff phenomenon is a sharp transition in the convergence to equilibrium of certain Markov chains. Despite the accumulation of several examples, a general theory is still missing, and identifying the mechanisms underlying this remarkable phenomenon constitutes one of the most fundamental open problems in the area of mixing times. After a brief introduction to this question, I will present a new approach based on the notion of "varentropy", and use it to effortlessly deduce cutoff for a broad class of Markov chains with non-negative curvature, including random walks on almost all Abelian Cayley graphs.