The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI

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DUEÑEZ, Eduardo, Duc K. HUYNH, Jon P. KEATING, Steven J. MILLER, Nina C. SNAITH, 2010. The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI. In: Journal of Physics A: Mathematical and Theoretical. 43(40), 405204. ISSN 1751-8113. eISSN 1751-8121

@article{Duenez2010lowes-25391, title={The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI}, year={2010}, doi={10.1088/1751-8113/43/40/405204}, number={40}, volume={43}, issn={1751-8113}, journal={Journal of Physics A: Mathematical and Theoretical}, author={Dueñez, Eduardo and Huynh, Duc K. and Keating, Jon P. and Miller, Steven J. and Snaith, Nina C.}, note={Article Number: 405204} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/25391"> <dc:contributor>Keating, Jon P.</dc:contributor> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-12-10T11:01:48Z</dcterms:available> <dc:language>eng</dc:language> <dcterms:title>The lowest eigenvalue of Jacobi random matrix ensembles and Painlevé VI</dcterms:title> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-12-10T11:01:48Z</dc:date> <dc:creator>Miller, Steven J.</dc:creator> <dc:creator>Snaith, Nina C.</dc:creator> <dc:creator>Huynh, Duc K.</dc:creator> <dc:creator>Keating, Jon P.</dc:creator> <dc:contributor>Snaith, Nina C.</dc:contributor> <dc:contributor>Huynh, Duc K.</dc:contributor> <dcterms:issued>2010</dcterms:issued> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/25391"/> <dcterms:bibliographicCitation>Journal of Physics A : Mathematical and Theoretical ; 43 (2010), 40. - 405204</dcterms:bibliographicCitation> <dc:contributor>Miller, Steven J.</dc:contributor> <dc:creator>Dueñez, Eduardo</dc:creator> <dc:contributor>Dueñez, Eduardo</dc:contributor> <dc:rights>deposit-license</dc:rights> <dcterms:abstract xml:lang="eng">We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painlevé VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painlevé VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.</dcterms:abstract> </rdf:Description> </rdf:RDF>

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