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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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References:
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