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| We consider a metastable diffusion moving in a multiwell potential on the rescaled n-dimensional integer lattice. From a spectral point of view metastability effects correspond to the presence of nearly degenerate small eigenvalues of the generator, each one linked to a well of the potential. In this talk a result providing complete asymptotic expansions of these small eigenvalues is presented. The proof, inspired by previous work of B. Helffer, M. Klein and F. Nier in continuous space setting, is based on tools of semiclassical analysis (Harmonic approximation, WKB expansions) and on a supersymmetric extension \`{a} la Witten of the generator on the level of discrete 1-forms. |
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