BULK 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 or complex Hermitian Wigner matrix and V is 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 local statistics in the bulk of the spectrum are universal in the limit of large N
Publisher
INST MATHEMATICAL STATISTICS
Issue Date
2016-05
Language
English
Article Type
Article
Keywords

GAUSSIAN RANDOM MATRICES; LARGE-N LIMIT; LOCAL EIGENVALUE STATISTICS; DENSITY-OF-STATES; EXTERNAL SOURCE; ORTHOGONAL POLYNOMIALS; SEMICIRCLE LAW; EXPONENTIAL WEIGHTS; FREE PROBABILITY; BETA-ENSEMBLES

Citation

ANNALS OF PROBABILITY, v.44, no.3, pp.2349 - 2425

ISSN
0091-1798
DOI
10.1214/15-AOP1023
URI
http://hdl.handle.net/10203/209493
Appears in Collection
MA-Journal Papers(저널논문)
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