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 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.
@incollection{JEDP_2014____A6_0,
author = {Bony, Jean-Fran\c{c}ois and H\'erau, Fr\'ed\'eric and Michel, Laurent},
title = {Tunnel effect for semiclassical random walk},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {6},
pages = {1--18},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2014},
doi = {10.5802/jedp.109},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.109/}
}
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 SP - 1 EP - 18 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.109/ DO - 10.5802/jedp.109 LA - en ID - JEDP_2014____A6_0 ER -
%0 Journal Article %A Bony, Jean-François %A Hérau, Frédéric %A Michel, Laurent %T Tunnel effect for semiclassical random walk %J Journées équations aux dérivées partielles %D 2014 %P 1-18 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.109/ %R 10.5802/jedp.109 %G en %F JEDP_2014____A6_0
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://www.numdam.org/articles/10.5802/jedp.109/
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