Probabilistic Weyl laws for quantized tori

Details Probabilistic Weyl laws for quantized tori Probabilistic Weyl laws for quantized tori

2009-09-10

arxiv.org/abs/0909.2014v2

Mathematics

Spectral Theory

33 pages, 3 figures, v2 corrected listed title

Scientific paper

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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