Almost Sure Weyl Law for Quantized Tori

被引：3

作者：

Vogel, Martin ^{[1
,2
]}

机构：

[1] Univ Strasbourg, UMR 7501, Inst Rech Math Avancee, 7 Rue Rene Descartes, F-67084 Strasbourg, France

[2] CNRS, 7 Rue Rene Descartes, F-67084 Strasbourg, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2020年 / 378卷 / 02期

关键词：

D O I：

10.1007/s00220-020-03797-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the eigenvalues of the Toeplitz quantization of complex-valued functions on the torus subject to small random perturbations given by a complex-valued random matrix whose entries are independent copies of a random variable with mean 0, variance 1 and bounded fourth moment. We prove that the eigenvalues of the perturbed operator satisfy a Weyl law with probability close to one, which proves in particular a conjecture by Christiansen and Zworski (Commun Math Phys 299:305-334, 2010).

引用

页码：1539 / 1585

页数：47

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