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Metastability of reversible random walks in potential fields. (English) Zbl 1327.82039
Summary: Let \(\Xi \) be an open and bounded subset of \({\mathbb {R}}^d \), and let \(F:\Xi \to {\mathbb {R}} \) be a twice continuously differentiable function. Denote by \(\Xi_N \) the discretization of \(\Xi \), \(\Xi_N = \Xi \cap (N^{-1} {\mathbb {Z}}^d) \), and denote by \(X_N(t) \) the continuous-time, nearest-neighbor, random walk on \(\Xi_N \) which jumps from \({\mathbf{x}} \) to \({\mathbf{y}}\) at rate \( e^{-(1/2) N [F({\mathbf{y}}) - F({\mathbf{x}})]} \). We examine in this article the metastable behavior of \(X_N(t) \) among the wells of the potential \(F \).

MSC:
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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