Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles

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dc.creatorForrester, P. J.
dc.creatorWitte, N. S.
dc.date2000-09-14
dc.date.accessioned2026-07-07T04:28:00Z
dc.date.available2026-07-07T04:28:00Z
dc.descriptionRandom matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form $a(s) e^{-b(s)}$ for $a$ simply related to a Painlevé transcendent and $b$ its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements).
dc.description6 pages, Latex2e
dc.identifierhttps://arxiv.org/abs/math-ph/0009023
dc.identifierhttp://arxiv.org/abs/math-ph/0009023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56628
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subject15A52; 34A34; 34A05; 33C45
dc.titleExact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles
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