# Weyl law for semi-classical resonances with randomly perturbed potentials / Johannes Sjöstrand

- Author:
- Sjöstrand, J. (Johannes)
- Published:
- Paris : Société mathématique de France, 2014.
- Copyright Date:
- ©2014
- Physical Description:
- vi, 144 pages ; 24 cm.

- Series:
- Mémoires de la SMF ; 136
- Contents:
- 1. Introduction -- 2. The result -- 3. Some elements of the proof -- 4. Grushin problems and determinants -- 5. Complex dilations -- 6. Semi-classical Sobolev spaces -- 7. Reductions to O and to derivative O -- 8. Some ODE preparations -- 9. Parametrix for the exterior Dirichlet problem -- 10. Exterior Poisson operator and DN map -- 11. The interior DN map -- 12. Some determinants -- 13. Upper bounds on the basic determinant -- 14. Some estimates for P[subscipt]out -- 15. Perturbation matrices and their singular values -- 16. End of the construction -- 17. End of the proof of theorem 2.2 and proof of proposition 2.4 -- A. WKB estimates on an interval.
- Summary:
- In this work we consider semi-classical Schrödinger operators with potentials supported in a bounded strictly convex subset O of R n with smooth boundary. Letting h denote the semi-classical parameter, we consider certain classes of small random perturbations and show that with probability very close to 1, the number of resonances in rectangles [a, b]-i[0,ch 2/3], is equal to the number of eigenvalues in [a, b] of the Dirichlet realization of the unperturbed operator in O up to a small remainder.
- Subject(s):
- ISBN:
- 2856297803 and 9782856297803
- Bibliography Note:
- Includes bibliographical references.

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