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arXiv · 1401.2935

Tunnel effect for semiclassical random walk

J. -F. Bony·F. Hérau·L. Michel
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Abstract

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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J. -F. Bony, F. Hérau, L. Michel. 2014-01-13. Tunnel effect for semiclassical random walk. https://doi.org/10.2140/apde.2015.8.289

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