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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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10.1007/bf00488120

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1432-0916

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Probabilistic Weyl Laws for Quantized Tori

Authors: T J Christiansen M Zworski
Publish Date: 2010/04/18
Volume: 299, Issue: 2, Pages: 305-334
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Abstract

For the Toeplitz quantization of complexvalued functions on a 2ndimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law 13 In numerical experiments the same Weyl law also holds for “false” eigenvalues created by pseudospectral effectsWe would like to thank Edward Bierstone and Pierre Milman for helpful discussions of Łojasiewicz inequalities Mark Rudelson for suggestions concerning random matrices and Stéphane Nonnenmacher and Michael Van Valkenburgh for comments on early versions of the paper The authors gratefully acknowledge the partial support by an MU research leave and NSF grants DMS 0500267 DMS 0654436 The first author thanks the Mathematics Department of UC Berkeley for its hospitality in spring 2009This article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team

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  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
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  7. Wall-Crossing, Free Fermions and Crystal Melting
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  9. Laminar Boundary Layers in Convective Heat Transport
  10. There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group
  11. Duality of 2D Gravity as a Local Fourier Duality
  12. Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities
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  15. Phase Boundaries in Algebraic Conformal QFT
  16. On the Singularity of the Free Energy at a First Order Phase Transition
  17. Free Analog of Pressure and Its Legendre Transform
  18. Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles
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  26. A Monoidal Category for Perturbed Defects in Conformal Field Theory
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