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Tunnel effect for semiclassical random walk

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arxiv 1401.2935 v1 pith:AF7YVB6D submitted 2014-01-13 math.AP math.PRmath.SP

J.-F. Bony , F. Hérau , L. Michel This is my paper
classification math.APmath.PRmath.SP
keywords semiclassicaleigenvaluesrandomwalkallowsapproachassociatedasymptotic
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We study a semiclassical random walk with respect to a probability measure with a finite number n_0 of wells. We show that the associated operator has exactly n_0 exponentially close to 1 eigenvalues (in the semiclassical sense), and that the other are O(h) away from 1. We also give an asymptotic of these small eigenvalues. The key ingredient in our approach is a general factorization result of pseudodifferential operators, which allows us to use recent results on the Witten Laplacian.

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