Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles

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dc.creatorForrester, P. J.
dc.date2000-05-30
dc.date.accessioned2026-07-07T05:32:52Z
dc.date.available2026-07-07T05:32:52Z
dc.descriptionThe scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles is evaluated in terms of a Painlevé V transcendent. This same Painlevé V transcendent is known from the work of Tracy and Widom, where it has been shown to specify the scaled distribution of the smallest eigenvalue in the Laguerre unitary ensemble. The starting point for our calculation is the scaled $k$-point distribution of every odd labelled eigenvalue in two superimposed Laguerre orthogonal ensembles.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/nlin/0005064
dc.identifierhttp://arxiv.org/abs/nlin/0005064
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79811
dc.subjectExactly Solvable and Integrable Systems
dc.titlePainlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles
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