Mémoires de la Société Mathématique de France 2014; 144 pp; softcover Number: 136 ISBN10: 2856297803 ISBN13: 9782856297803 List Price: US$52 Member Price: US$41.60 Order Code: SMFMEM/136
 The author considers semiclassical Schrödinger operators with potentials supported in a bounded strictly convex subset \(\mathcal{O}\) of \(\mathbb{R}^n\) with smooth boundary. Letting \(h\) denote the semiclassical 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. Table of Contents  Introduction
 The result
 Some elements of the proof
 Grushin problems and determinants
 Complex dilations
 Semiclassical Sobolev spaces
 Reductions to \(\mathcal{O}\) and to \(\partial\mathcal{O}\)
 Some ODE preparations
 Parametrix for the exterior Dirichlet problem
 Exterior Poisson operator and DN map
 The interior DN map
 Some determinants
 Upper bounds on the basic determinant
 Some estimates for \(P_\mathrm{out}\)
 Perturbation matrices and their singular values
 End of the construction
 End of the proof of Theorem 2.2 and proof of Proposition 2.4
 Appendix. WKB estimates on an interval
 Bibliography
