Higher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy

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dc.creatorClaeys, T.
dc.creatorIts, A.
dc.creatorKrasovsky, I.
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:31:04Z
dc.date.available2026-07-07T12:31:04Z
dc.descriptionWe study Fredholm determinants related to a family of kernels which describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher order analogues of the Airy kernel and are built out of functions associated with the Painlevé I hierarchy. The Fredholm determinants related to those kernels are higher order generalizations of the Tracy-Widom distribution. We give an explicit expression for the determinants in terms of a distinguished smooth solution to the Painlevé II hierarchy. In addition we compute large gap asymptotics for the Fredholm determinants.
dc.description45 pages
dc.identifierhttps://arxiv.org/abs/0901.2473
dc.identifierhttp://arxiv.org/abs/0901.2473
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216330
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subject33E17; 35Q15
dc.titleHigher order analogues of the Tracy-Widom distribution and the Painleve II hierarchy
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