Djalil Chafaï: Aspects of the Cutoff Phenomenon for Diffusions

Abstract:

The cutoff phenomenon, conceptualized in the context of finite Markov chains, states that for certain linear evolution equations, started from a point, the distance towards a long time equilibrium may become more and more abrupt in high dimensional state spaces and for certain choices of initial conditions. This can be seen as a critical competition between trend to equilibrium and initial condition. This talk is about the cutoff phenomenon for a few classes of linear and nonlinear diffusions.