Tunnel effect for semiclassical random walk
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.

@article{JEDP_2014____A6_0,
     author = {Bony, Jean-Fran\c cois and H\'erau, Fr\'ed\'eric and Michel, Laurent},
     title = {Tunnel effect for semiclassical random walk},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2014},
     doi = {10.5802/jedp.109},
     language = {en},
     url = {http://www.numdam.org/item/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/item/JEDP_2014____A6_0/

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