General Toeplitz matrices subject to Gaussian perturbations

Johannes Sjoestrand; Martin Vogel

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arXiv · 1905.10265

General Toeplitz matrices subject to Gaussian perturbations

Johannes Sjoestrand·Martin Vogel

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Abstract

We study the spectra of general $N\times N$ Toeplitz matrices given by symbols in the Wiener Algebra perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove an asymptotic formula for the number of eigenvalues of the perturbed matrix in smooth domains. We show that these eigenvalues follow a Weyl law with probability sub-exponentially close to $1$, as $N\gg1$, in particular that most eigenvalues of the perturbed Toeplitz matrix are close to the curve in the complex plane given by the symbol of the unperturbed Toeplitz matrix.

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BibTeX RIS

Johannes Sjoestrand, Martin Vogel. 2019-05-24. General Toeplitz matrices subject to Gaussian perturbations. https://arxiv.org/abs/1905.10265

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