Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrum of random perturbations of Toeplitz matrices with finite
  symbols   Let $T_N$ denote an $N\times N$ Toeplitz matrix with finite, $N$ independent
symbol ${\bf a}$. For $E_N$ a noise matrix satisfying mild assumptions
(ensuring, in particular, that $N^{-1/2}\|E_N\|_{{\rm HS}}\to_{N\to\infty} 0$
at a polynomial rate), we prove that the empirical measure of eigenvalues of
$T_N+E_N$ converges to the law of ${\bf a}(U)$, where $U$ is uniformly
distributed on the unit circle in the complex plane. This extends results from
arXiv:1712.00042 to the non-triangular setup and non complex Gaussian noise,
and confirms predictions obtained in Reichel and Trefethen (1992) using the
notion of pseudo-spectrum.

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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: chem-ph