Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The outliers of a deformed Wigner matrix   We derive the joint asymptotic distribution of the outlier eigenvalues of an
additively deformed Wigner matrix $H$. Our only assumptions on the deformation
are that its rank be fixed and its norm bounded. Our results extend those of
[The isotropic semicircle law and deformation of Wigner matrices. Preprint] by
admitting overlapping outliers and by computing the joint distribution of all
outliers. In particular, we give a complete description of the failure of
universality first observed in [Ann. Probab. 37 (2009) 1-47; Ann. Inst. Henri
Poincar\'{e} Probab. Stat. 48 (1013) 107-133; Free convolution with a
semi-circular distribution and eigenvalues of spiked deformations of Wigner
matrices. Preprint]. We also show that, under suitable conditions, outliers may
be strongly correlated even if they are far from each other. Our proof relies
on the isotropic local semicircle law established in [The isotropic semicircle
law and deformation of Wigner matrices. Preprint]. The main technical
achievement of the current paper is the joint asymptotics of an arbitrary
finite family of random variables of the form
$\langle\mathbf{v},(H-z)^{-1}\mathbf{w}\rangle$.

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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con