Tunnel effect for semiclassical random walk
Jean-François Bony1 ; Frédéric Hérau2 ; Laurent Michel3
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.

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
Jean-François Bony 1 ; Frédéric Hérau 2 ; Laurent Michel 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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Jean-François Bony; Frédéric Hérau; Laurent Michel. Tunnel effect for semiclassical random walk. Journées équations aux dérivées partielles (2014), article  no. 6, 18 p. doi : 10.5802/jedp.109. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.109/

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