{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1390282680205479040.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.2206/kyushujm.61.457"}},{"identifier":{"@type":"URI","@value":"https://www.jstage.jst.go.jp/article/kyushujm/61/2/61_2_457/_pdf"}},{"identifier":{"@type":"NAID","@value":"110006377561"}}],"dc:title":[{"@language":"en","@value":"THE DISTRIBUTION OF THE FIRST EIGENVALUE SPACING AT THE HARD EDGE OF THE LAGUERRE UNITARY ENSEMBLE"}],"dc:language":"en","description":[{"type":"abstract","notation":[{"@language":"en","@value":"The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlevé V system, and the solution of its associated linear isomonodromic system. In particular, it is characterized by the polynomial solutions to the isomonodromic equations which are also orthogonal with respect to a deformation of the Laguerre weight. In the scaling to the hard edge regime we find an analogous situation where a certain Painlevé III' system and its associated linear isomonodromic system characterize the scaled distribution. We undertake extensive analytical studies of this system and use this knowledge to accurately compute the distribution and its moments for various values of the parameter <I>a</I>. In particular, choosing <I>a</I> = ±1/2 allows the first eigenvalue spacing distribution for random real orthogonal matrices to be computed."}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1410282680205479040","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000021595881"}],"foaf:name":[{"@language":"en","@value":"WITTE Nicholas S."}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of Mathematics and Statistics University of Melbourne"}]},{"@id":"https://cir.nii.ac.jp/crid/1410282680205479041","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000021595876"}],"foaf:name":[{"@language":"en","@value":"FORRESTER Peter J."}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of Mathematics and Statistics University of Melbourne"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"13406116"},{"@type":"EISSN","@value":"18832032"},{"@type":"NCID","@value":"AA10994346"}],"prism:publicationName":[{"@language":"en","@value":"Kyushu Journal of Mathematics"},{"@language":"en","@value":"Kyushu J. Math."},{"@language":"ja","@value":"九州数学雑誌"}],"dc:publisher":[{"@language":"en","@value":"Faculty of Mathematics, Kyushu University"},{"@language":"ja","@value":"九州大学大学院数理学研究院"}],"prism:publicationDate":"2007","prism:volume":"61","prism:number":"2","prism:startingPage":"457","prism:endingPage":"526"},"reviewed":"false","url":[{"@id":"https://www.jstage.jst.go.jp/article/kyushujm/61/2/61_2_457/_pdf"},{"@id":"http://hdl.handle.net/2324/11778"}],"availableAt":"2007","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=random%20matrices","dc:title":"random matrices"},{"@id":"https://cir.nii.ac.jp/all?q=eigenvalue%20distribution","dc:title":"eigenvalue distribution"},{"@id":"https://cir.nii.ac.jp/all?q=Wishart%20matrices","dc:title":"Wishart matrices"},{"@id":"https://cir.nii.ac.jp/all?q=Painlev%C3%A9%20equations","dc:title":"Painlevé equations"},{"@id":"https://cir.nii.ac.jp/all?q=isomonodromic%20deformations","dc:title":"isomonodromic deformations"}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360001114002652416","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Painlevé Differential Equations in the Complex Plane"}]},{"@id":"https://cir.nii.ac.jp/crid/1360005515745860096","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Janossy densities for chiral random matrix ensembles and their applications to two-color QCD"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292619972656384","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"THE METHOD OF ISOMONODROMY DEFORMATIONS AND THE ASYMPTOTICS OF SOLUTIONS OF THE “COMPLETE” THIRD PAINLEVÉ EQUATION"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292620024048896","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Asymptotics of Orthogonal Polynomials: Some Old, Some New, Some Identities"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574093685042176","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The spectrum edge of random matrix ensembles"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574094285775104","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Zeroes of zeta functions and symmetry"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095638205056","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574096074649984","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Exact Scaling Functions for One-Dimensional Stationary KPZ Growth"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569304103296","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Exact results and universal asymptotics in the Laguerre random matrix ensemble"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137043503991936","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The spectrum of the Dirac operator near zero virtuality for Nc = 2 and chiral random matrix theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137045937942528","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the solvability of Painleve I, III and V"}]},{"@id":"https://cir.nii.ac.jp/crid/1361699995756740224","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fredholm determinants, differential equations and matrix models"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981469233936640","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. 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