Geodesic
Tunnel effect for semiclassical random walk
Bony, Jean-François1  ; Hérau, Frédéric2  ; Michel, Laurent3
1 Institut Mathématiques de Bordeaux Université de Bordeaux, UMR CNRS 5251 351, cours de la Libération 33405 Talence Cedex, France
2 Laboratoire de Mathématiques Jean Leray Université de Nantes, UMR CNRS 6629 2, rue de la Houssinière 44322 Nantes Cedex 03, France
3 Laboratoire Jean-Alexandre Dieudonné Université de Nice - Sophia Antipolis UMR CNRS 7351 06108 Nice Cedex 02, France
Journées équations aux dérivées partielles (2014), article no. 6, 18 p.

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In this note we describe recent results on semiclassical random walk associated to a probability density which may also concentrate as the semiclassical parameter goes to zero. The main result gives a spectral asymptotics of the close to 1 eigenvalues. This problem was studied in [1] and relies on a general factorization result for pseudo-differential operators. In this note we just sketch the proof of this second theorem. At the end of the note, using the factorization, we give a new proof of the spectral asymptotics based on some comparison argument.

DOI : 10.5802/jedp.109

Bony, Jean-François 1 ; Hérau, Frédéric 2 ; Michel, Laurent 3

1 Institut Mathématiques de Bordeaux Université de Bordeaux, UMR CNRS 5251 351, cours de la Libération 33405 Talence Cedex, France
2 Laboratoire de Mathématiques Jean Leray Université de Nantes, UMR CNRS 6629 2, rue de la Houssinière 44322 Nantes Cedex 03, France
3 Laboratoire Jean-Alexandre Dieudonné Université de Nice - Sophia Antipolis UMR CNRS 7351 06108 Nice Cedex 02, France 
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Bony, Jean-François; Hérau, Frédéric; Michel, Laurent. Tunnel effect for semiclassical random walk. Journées équations aux dérivées partielles (2014), article  no. 6, 18 p. doi : 10.5802/jedp.109. http://geodesic.mathdoc.fr/articles/10.5802/jedp.109/

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