Metastability And Typical Exit Paths In Stochastic Dynamics

In this paper we review and discuss results on metastability. We consider ergodic aperiodic Markov chains with exponentially small transition probabilities and we give a complete description of the typical tube of trajectories during the first excursion outside a general domain Q. 25=aprile=1997 [1] 0:1 Section 1. Introduction. In this review we want to describe some recent results in the theory of metastability from the point of view of mathematical physics and probability theory. Mathematically we will deal with the study of some large deviation problems for families of Markov chains with finite state space and transition probabilities decaying exponentially fast in a large external parameter fi: the so called Freidlin-Wentzell regime. From physical point of view we analyze a central problem arising in the dynamical description of phase transitions: the decay from metastable to stable equilibrium. Phase transitions (like, for instance, liquid-vapour for a fluid or positive-negativ..