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arXiv · 0909.2014

Probabilistic Weyl laws for quantized tori

T. J. Christiansen·M. Zworski
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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. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.

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T. J. Christiansen, M. Zworski. 2009-09-11. Probabilistic Weyl laws for quantized tori. https://doi.org/10.1007/s00220-010-1047-2

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