Kolloquien und Oberseminare Übersicht Detail

Speaker:
Prof. Dr. Michael Högele (Universidad de los Andes, Kolumbien)

Abstract: Many stochastic systems - think of strongly irreducible Markov chains on finite state space - have the tendency to converge (in some metric) as a function of time to a unique dynamical equilibrium. In this talk we give a short introduction to the so-called cutoff phenomenon for systems which depend on a parameter (for instance, the growing size of the state space or the decreasing noise intensity). It states that in terms of this parameter the system converges sharply along a precise deterministic time scale. That is, morally speaking, any lag behind this time scale implies large distances to the equilibrium, while any advance ahead of this time scale leads to small distances. We explain recent results on the topic for a variety of linear and nonlinear ordinary and partial differential equations with a stable state for small noise in the Wasserstein distance. These results are part of an ongoing research project with G. Barrera (U. Helsinki) and J.C. Pardo (CIMAT, Mexico).