Edge universality for deformed Wigner matrices

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We consider N x N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution F-1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2015-09
Language
English
Article Type
Review
Citation

REVIEWS IN MATHEMATICAL PHYSICS, v.27, no.8

ISSN
0129-055X
DOI
10.1142/S0129055X1550018X
URI
http://hdl.handle.net/10203/205341
Appears in Collection
MA-Journal Papers(저널논문)
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