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Tunnel effect for
semiclassical random walks
Jean-François Bony, Frédéric Hérau and Laurent Michel |
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Vol. 8 (2015), No. 2, 289–332
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Abstract |
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We study a semiclassical random walk with respect to a probability measure with a finite number of wells. We show that the associated operator has exactly eigenvalues exponentially close to (in the semiclassical sense), and that the others are away from . 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
analysis of PDEs, probability, spectral theory
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Mathematical Subject Classification 2010
Primary: 35S05, 35P15, 47A10, 60J05
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Milestones
Received: 22 January 2014
Revised: 9 January 2015
Accepted: 9 February 2015
Published: 10 May 2015
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Authors |
| Jean-François Bony | |
| Institut Mathématiques de
Bordeaux Université de Bordeaux 351, cours de la Libération 33405 Talence France |
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| Frédéric Hérau | |
| Laboratoire de Mathématiques Jean
Leray Université de Nantes 2, rue de la Houssinière 44322 Nantes France |
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| Laurent Michel | |
| Laboratoire J. A.
Dieudonné Université de Nice Parc Valrose 06000 Nice France |
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