Probabilistic Weyl Laws for Quantized Tori
Communications in Mathematical Physics(2010)
摘要
For the Toeplitz quantization of complex-valued functions on a 2 n -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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关键词
Random Matrix,Pseudodifferential Operator,Random Matrix Theory,Toeplitz Matrice,Symbol Class
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