Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General Toeplitz matrices subject to Gaussian perturbations   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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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph