Tunnel effect for semiclassical random walk
Analysis of PDEs
2016-01-20 v1 Probability
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1401.2935,
title = {Tunnel effect for semiclassical random walk},
author = {J. -F. Bony and F. Hérau and L. Michel},
journal= {arXiv preprint arXiv:1401.2935},
year = {2016}
}