**Memoires de la Societe Mathematique de France**

Volume: 136;
2014;
144 pp;
Softcover

MSC: Primary 81; 35;
**Print ISBN: 978-2-85629-780-3
Product Code: SMFMEM/136**

List Price: $52.00

Individual Member Price: $41.60

# Weyl Law for Semi-Classical Resonances with Randomly Perturbed Potentials

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*Johannes Sjöstrand*

A publication of the Société Mathématique de France

The author considers semi-classical Schrödinger operators with potentials supported in a bounded strictly convex subset \(\mathcal{O}\) of \(\mathbb{R}^n\) with smooth boundary. Letting \(h\) denote the semi-classical parameter, the author considers classes of small random perturbations and shows that with probability very close to 1, the number of resonances in rectangles \([a,b]-i[0,ch^{\frac 23}\)] is equal to the number of eigenvalues in \([a,b]\) of the Dirichlet realization of the unperturbed operator in \(\mathcal{O}\) up to a small remainder.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians.