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dc.contributor.authorHolcomb, Diane
dc.contributor.authorValkó, Benedek
dc.date.accessioned2017-09-14T21:37:54Z
dc.date.available2017-09-14T21:37:54Z
dc.date.issued2017-08
dc.identifier.citationOvercrowding asymptotics for the Sine(beta) process 2017, 53 (3):1181 Annales de l'Institut Henri Poincaré, Probabilités et Statistiquesen
dc.identifier.issn0246-0203
dc.identifier.doi10.1214/16-AIHP752
dc.identifier.urihttp://hdl.handle.net/10150/625509
dc.description.abstractWe give overcrowding estimates for the Sine(beta) process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having exactly n points in a fixed interval is given by e(-beta/2n2) log(n)+O(n(2)) as n -> infinity. We also identify the next order term in the exponent if the size of the interval goes to zero.
dc.description.sponsorshipNational Science Foundation CAREER award [DMS-1053280]en
dc.language.isoenen
dc.publisherINST MATHEMATICAL STATISTICSen
dc.relation.urlhttp://projecteuclid.org/euclid.aihp/1500624035en
dc.rights© Association des Publications de l’Institut Henri Poincaré, 2017en
dc.subjectbeta-ensemblesen
dc.subjectRandom matricesen
dc.subjectOvercrowdingen
dc.titleOvercrowding asymptotics for the Sine(beta) processen
dc.typeArticleen
dc.contributor.departmentUniv Arizona, Dept Mathen
dc.identifier.journalAnnales de l'Institut Henri Poincaré, Probabilités et Statistiquesen
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en
dc.eprint.versionFinal published versionen
refterms.dateFOA2018-06-29T21:41:01Z
html.description.abstractWe give overcrowding estimates for the Sine(beta) process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having exactly n points in a fixed interval is given by e(-beta/2n2) log(n)+O(n(2)) as n -> infinity. We also identify the next order term in the exponent if the size of the interval goes to zero.


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