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• W2951692878 abstract "Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by adding a random finite rank matrix with delocalized eigenvectors and study the extreme eigenvalues of the deformed model. We give necessary conditions on the deterministic matrix X_n so that the eigenvalues converging out of the bulk exhibit Gaussian fluctuations, whereas the eigenvalues sticking to the edges are very close to the eigenvalues of the non-perturbed model and fluctuate in the same scale. We generalize these results to the case when X_n is random and get similar behavior when we deform some classical models such as Wigner or Wishart matrices with rather general entries or the so-called matrix models." @default.
• W2951692878 created "2019-06-27" @default.
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• W2951692878 date "2010-09-01" @default.
• W2951692878 modified "2023-09-27" @default.
• W2951692878 title "Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices" @default.
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