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A Note on the Eigenvalue Density of Random Matrices

✍ Scribed by Michael K.-H. Kiessling; Herbert Spohn


Publisher
Springer
Year
1999
Tongue
English
Weight
114 KB
Volume
199
Category
Article
ISSN
0010-3616

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be Hermitian matrices with eigenvalues Ξ» 1 β€’ β€’ β€’ Ξ» k and Ξ» 1 β€’ β€’ β€’ Ξ» k , respectively. Denote by E the spectral norm of the matrix E, and Ξ· the spectral gap between the spectra of H 1 and H 2 . It is shown that , which improves all the existing results. Similar bounds are obtained for singular valu