02-438 Michael Eckhoff

Precise Asymptotics of Small Eigenvalues of Reversible Diffusions in the Metastable Regime (442K, postscript) Oct 29, 02

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Abstract. We investigate the connection between metastability and the spectrum near zero corresponding to the elliptic, second-order, differential operator $L_\e\equiv -\e\D+\nabla F\cdot\nabla$, $\e>0$, with $F:\R^d\to\R$. For generic $F$ to each local minimum of $F$ there corresponds an eigenvalue of $L_\e$ which converges to zero exponentially fast as $\e\downarrow 0$. Modulo errors of exponentially small order in $\e$ this eigenvalue is given as the inverse of the expected metastable relaxation time. The corresponding eigenstate, which may be viewed as a metastable state, is highly concentrated in the basin of attraction of this trap.

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