University of Maryland

**Abstract**: We characterize metastability for a small random
perturbation of a nearly-Hamiltonian system. We use the averaging principle
and the theory of large deviations to prove that the metastable ``state" is, in
general, not a single state but rather a probability measure across the stable
equilibria of the unperturbed Hamiltonian system. The set of all metastable
states is a finite set that is independent of the stochastic perturbation.

This is joint work with Mark Freidlin, to appear in the journal Stochastics and Dynamics.