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.