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- W4297173728 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.
- W4297173728 created "2022-09-27" @default.
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- W4297173728 date "2010-09-01" @default.
- W4297173728 modified "2023-10-16" @default.
- W4297173728 title "Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices" @default.
- W4297173728 doi "https://doi.org/10.48550/arxiv.1009.0145" @default.
- W4297173728 hasPublicationYear "2010" @default.
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