Gaussian fluctuations for linear spectral statistics of deformed Wigner matrices

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We consider large-dimensional Hermitian or symmetric random matrices of the form W = M + theta V, where M is a Wigner matrix and V is a real diagonal matrix whose entries are independent of M. For a large class of diagonal matrices V, we prove that the fluctuations of linear spectral statistics of W for C-2 test function can be decomposed into that of M and of V, and that each of those weakly converges to a Gaussian distribution. We also calculate the formulae for the means and variances of the limiting distributions.
Publisher
WORLD SCI PUBL CO INC
Issue Date
2020-07
Language
English
Article Type
Article
Citation

RANDOM MATRICES-THEORY AND APPLICATIONS, v.9, no.3

ISSN
2010-3263
DOI
10.1142/S2010326320500112
URI
http://hdl.handle.net/10203/281977
Appears in Collection
MA-Journal Papers(저널논문)
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