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Probabilistic Weyl Laws for Quantized Tori

  • Author(s): Christiansen, T. J.
  • Zworski, M.
  • et al.
Abstract

For the Toeplitz quantization of complex-valued functions on a 2n-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law (1.3). In numerical experiments the same Weyl law also holds for “false” eigenvalues created by pseudospectral effects.

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