### Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues

We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form $-\u03f5\Delta +\nabla F(\xb7)\nabla $ on ${\mathbb{R}}^{d}$ or subsets of ${\mathbb{R}}^{d}$, where $F$ is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum...