Metastability in reversible diffusion processes

The overdamped motion of a Brownian particle in a potential landscape with multiple wells is known to exhibit metastability, i.e., for weak noise, transitions between potential minima occur on exponentially long time scales. The small-noise asymptotics of transition times is usually described by the Eyring-Kramers formula. However, this formula breaks down in the presence of degenerate (non-quadratic) saddles or wells. We will show how recent results by Bovier, Eckhoff, Gayrard and Klein, providing the first rigorous proof of the Eyring-Kramers formula, can be extended to degenerate landscapes.

This is joint work with Nils Berglund (Orléans).