Advertisement

Distribution of Eigenvalues for Semi-classical Elliptic Operators with Small Random Perturbations, Results and Outline

  • Johannes Sjöstrand
Chapter
Part of the Pseudo-Differential Operators book series (PDO, volume 14)

Abstract

In this chapter we will state a result asserting that for elliptic semi-classical (pseudo-)differential operators the eigenvalues are distributed according to Weyl’s law “most of the time” in a probabilistic sense. The first three sections are devoted to the formulation of the results and in the last section we give an outline of the proof that will be carried out in Chaps.  16 and  17.

References

  1. 54.
    M. Hager, Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints. I. Un modèle. Ann. Fac. Sci. Toulouse Math. 15(2), 243–280 (2006)MathSciNetCrossRefGoogle Scholar
  2. 56.
    M. Hager, J. Sjöstrand, Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators. Math. Ann. 342(1), 177–243 (2008). http://arxiv.org/abs/math/0601381 MathSciNetCrossRefGoogle Scholar
  3. 137.
    J. Sjöstrand, Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations. Ann. Fac. Sci. Toulouse 18(4), 739–795 (2009). http://arxiv.org/abs/0802.3584 MathSciNetCrossRefGoogle Scholar
  4. 139.
    J. Sjöstrand, Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations. Ann. Fac. Sci. Toulouse 19(2), 277–301 (2010). http://arxiv.org/abs/0809.4182 MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johannes Sjöstrand
    • 1
  1. 1.Université de Bourgogne Franche-ComtéDijonFrance

Personalised recommendations