Estimates for moments of random matrices with Gaussian elements

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dc.creatorKhorunzhiy, O.
dc.date2005-07-22
dc.date2006-07-23
dc.date.accessioned2026-07-07T06:42:18Z
dc.date.available2026-07-07T06:42:18Z
dc.descriptionWe describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic example, we consider the GUE matrices. Immediate applications include GOE and the ensemble of Gaussian anti-symmetric Hermitian matrices. The estimates we derive give asymptotically exact expressions for the first terms of 1/N-expansions of the moments and covariance terms. We apply our method to the ensemble of Gaussian Hermitian random band matrices whose elements are zero outside of the band of width b. The estimates we obtain show that the spectral norm of these matrices remains bounded in the limit of infinite N when b is much greater than log N to the power 3/2.
dc.description45 pages (the version improved after the referee reports; one diagram added)
dc.identifierhttps://arxiv.org/abs/math-ph/0507060
dc.identifierhttp://arxiv.org/abs/math-ph/0507060
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101987
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject15A52;60F99
dc.titleEstimates for moments of random matrices with Gaussian elements
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