Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Perturbations of Matrix Polynomials   A sum of a large-dimensional random matrix polynomial and a fixed low-rank
matrix polynomial is considered. The main assumption is that the resolvent of
the random polynomial converges to some deterministic limit. A formula for the
limit of the resolvent of the sum is derived and the eigenvalues are localised.
Three instances are considered: a low-rank matrix perturbed by the Wigner
matrix, a product $HX$ of a fixed diagonal matrix $H$ and the Wigner matrix $X$
and a special matrix polynomial. The results are illustrated with various
examples and numerical simulations.

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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph