A potential theoretic approach for the analysis of stochastic metastable systems

Lunedi' 11 Giugno 2012 - A. Bianchi


Lunedi' 11 Giugno 2012, alle 15:00, nell'aula 2BC30 della Torre Archimede, la Dr.ssa Alessandra Bianchi (Universita' di Padova) terra' un seminario dal titolo "A potential theoretic approach for the analysis of stochastic metastable systems".

Metastability is a dynamical phenomenon taking place when some parameters of a (random or deterministic) system change, giving rise to a new equilibrium. It can be roughly characterized by the existence of at least two time scales, so that at a short time scale the system remains in a local apparent equilibrium while at longer (metastable) time scales, it moves to the new equilibrium. The main issue is then to characterize this metastable time scale.

In the context of Markovian stochastic dynamics, Bovier et al. have proposed in 2001 a new approach to the study of metastability, which is based on an electric network perspective of the dynamics and focus on the characterization of the metastable times via estimates on capacities, which are fundamental objects in potential theory.

In this talk we will first describe the main ideas and mathematical objects of this method, and recall some of the main results obtained so far by its implementation. Then we will present some recent results, obtained in collaboration with A. Gaudillière, where these ideas have been further developed to characterize, under simple hypotheses on the system, the average and the distributional law of metastable times, as well as to estimate the relaxation and mixing times of the dynamics. Some simple illustrative examples will be finally discussed.

Rif. int. P. Dai Pra