Tunnel effect for semiclassical random walk
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
Journées Équations aux dérivées partielles (2014)
- Volume: 8, Issue: 2, page 1-18
- ISSN: 0752-0360
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topBony, Jean-François, Hérau, Frédéric, and Michel, Laurent. "Tunnel effect for semiclassical random walk." Journées Équations aux dérivées partielles 8.2 (2014): 1-18. <http://eudml.org/doc/275423>.
@article{Bony2014,
abstract = {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.},
affiliation = {Institut Mathématiques de Bordeaux Université de Bordeaux, UMR CNRS 5251 351, cours de la Libération 33405 Talence Cedex, France; Laboratoire de Mathématiques Jean Leray Université de Nantes, UMR CNRS 6629 2, rue de la Houssinière 44322 Nantes Cedex 03, France; Laboratoire Jean-Alexandre Dieudonné Université de Nice - Sophia Antipolis UMR CNRS 7351 06108 Nice Cedex 02, France},
author = {Bony, Jean-François, Hérau, Frédéric, Michel, Laurent},
journal = {Journées Équations aux dérivées partielles},
keywords = {semiclassical random walks; tunnel effect; Markov transition kernel; pseudodifferential operators; spectral theory; Witten-Laplacian},
language = {eng},
number = {2},
pages = {1-18},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Tunnel effect for semiclassical random walk},
url = {http://eudml.org/doc/275423},
volume = {8},
year = {2014},
}
TY - JOUR
AU - Bony, Jean-François
AU - Hérau, Frédéric
AU - Michel, Laurent
TI - Tunnel effect for semiclassical random walk
JO - Journées Équations aux dérivées partielles
PY - 2014
PB - Groupement de recherche 2434 du CNRS
VL - 8
IS - 2
SP - 1
EP - 18
AB - 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.
LA - eng
KW - semiclassical random walks; tunnel effect; Markov transition kernel; pseudodifferential operators; spectral theory; Witten-Laplacian
UR - http://eudml.org/doc/275423
ER -
References
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