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Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach. (English) Zbl 1067.35057

Proceedings of the conference on partial differential equations, Forges-les-Eaux, France, June 7–11, 2004. Exp. I–XIII. Paris: Centre National de la Recherche Scientifique, Groupement de Recherche 2434 (ISBN 2-7302-1221-3/pbk). Exp. No. VIII, 17 p. (2004).
Summary: We present here a simplified version of recent results obtained by B. Helffer, M. Klein and the author [Mat. Contemp. 26, 41–85 (2004; Zbl 1079.58025)]. They are concerned with the exponentially small eigenvalues of the Witten Laplacian on 0-forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of \(\Delta^{(0)}_{f,h}\) and solves efficiently the question of weakly resonant wells.
For the entire collection see [Zbl 1055.00015].

MSC:

35P15 Estimates of eigenvalues in context of PDEs
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
58J10 Differential complexes

Citations:

Zbl 1079.58025
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