Metastability in irreversible diffusion processes and stochastic resonance

In the last few years, much progress has been made in the quantitative description of metastability in reversible diffusion processes. In particular, recent works by Bovier, Eckhoff, Gayrard and Klein have established precise relations between metastable lifetimes, the potential landscape, and small eigenvalues of the diffusion's generator, using potential theory.

The picture is much less precise for irreversible diffusions. In general, not even the invariant distribution is known.

For a class of irreversible two-dimensional diffusions, we shall discuss the diffusion-exit problem from domains whose boundary is an unstable periodic orbit. In such cases, the theory of large deviations yields no information on the distribution of exit locations. We derive this distribution explicitly, up to multiplicative errors in the prefactor.

As an application, we discuss the phenomenon of stochastic resonance, for which the result on exit distributions allows to determine a precise expression of the residence-time distribution.

Joint work with Barbara Gentz, WIAS, Berlin.