Abstract
The cutoff phenomenon is an abrupt transition from the non-equilibrium state to the equilibrium state undergone by certain Markov processes in the limit where the number of states tends to infinity. Discovered forty years ago in the context of card shuffling, it has since been established in a variety of contexts, including random walks on graphs and groups, high-temperature spin systems or interacting particles. Nevertheless, a general theory is still lacking, and identifying the general mechanisms underlying this mysterious phenomenon remains one of the most fundamental problems in the field of mixing times. My talk will provide a no-obligation introduction to this fascinating question and its recent links with the notions of entropy, curvature and concentration.
