Nier, Francis 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]. Cited in 2 Documents 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 Keywords:exponentially small eigenvalues; Witten Laplacian; Witten complex structure; weakly resonant wells Citations:Zbl 1079.58025 PDFBibTeX XMLCite \textit{F. Nier}, in: Journées ``Équations aux dérivées partielles'', Forges-les-Eaux, France, 7 au 11 juin 2004. Exposés Nos. I--XIII. Paris: Centre National de la Recherche Scientifique, Groupement de Recherche 2434. Exp. No. VIII, 17 p. (2004; Zbl 1067.35057) Full Text: Numdam