Metastability of reversible random walks in potential fields

Let $Ξ$ be an open and bounded subset of $\bb R^d$, and let $F:Ξ\to\bb R$ be a twice continuously differentiable function. Denote by $Ξ_N$ th discretization of $Ξ$, $Ξ_N = Ξ\cap (N^{-1} \bb Z^d)$, and denote by $X_N(t)$ the continuous-time, nearest-neighbor, random walk on $Ξ_N$ which jumps from $\bs x$ to $\bs y$ at rate $ e^{-(1/2) N [F(\bs y) - F(\bs x)]}$. We examine in this article the metastable behavior of $X_N(t)$ among the wells of the potential $F$.

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