Gaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields

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dc.creatorSoshnikov, Alexander B.
dc.date1999-07-15
dc.date1999-12-14
dc.date.accessioned2026-07-07T04:32:52Z
dc.date.available2026-07-07T04:32:52Z
dc.descriptionWe prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the Gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions. As another corollary of Costin-Lebowitz Theorem we prove CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.
dc.descriptionThe essential alterations are a slightly different formulation of the Costin-Lebowitz Theorem and the addition of Remark 4 in the section 2
dc.identifierhttps://arxiv.org/abs/math-ph/9907012
dc.identifierhttp://arxiv.org/abs/math-ph/9907012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58359
dc.subjectMathematical Physics
dc.subjectProbability
dc.titleGaussian fluctuation for the number of particles in Airy, Bessel, sine and other determinantal random point fields
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