Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity

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dc.contributor.author Charlier, Christophe
dc.contributor.author Deaño Cabrera, Alfredo
dc.date.accessioned 2021-02-24T09:55:44Z
dc.date.available 2021-02-24T09:55:44Z
dc.date.issued 2018-03-07
dc.identifier.bibliographicCitation SIGMA, (2018), v. 14, 018, [43] p.
dc.identifier.issn 1815-0659
dc.identifier.uri http://hdl.handle.net/10016/32009
dc.description This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14). The full collection is available at https://www.emis.de/journals/SIGMA/OPSFA2017.html
dc.description.abstract We study nxn Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We obtain large n asymptotics for these Hankel determinants, and we observe a critical transition when the size of the jumps varies with n. These determinants arise in the thinning of the generalised Gaussian unitary ensembles and in the construction of special function solutions of the Painlevé IV equation.
dc.description.sponsorship C. Charlier was supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007/2013)/ ERC Grant Agreement n. 307074. A. Deaño acknowledges financial support from projects MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P from the Spanish Ministry of Economy and Competitivity. The authors are grateful to A.B.J. Kuijlaars for sharing a simplified proof for the first part of [11, Proposition A.1]. This inspired us to simplify the proof of Lemma 7.4. We also thank T. Claeys for a careful reading of the introduction and for useful remarks. The authors acknowledge the referees for their careful reading and useful remarks.
dc.format.extent 43
dc.language.iso eng
dc.publisher Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine
dc.rights The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Asymptotic analysis
dc.subject.other Riemann-Hilbert problems
dc.subject.other Hankel determinants
dc.subject.other Random matrix theory
dc.subject.other Painlevé equations
dc.title Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
dc.type research article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.3842/SIGMA.2018.018
dc.rights.accessRights open access
dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7-ERC-307074
dc.relation.projectID Gobierno de España. MTM2015-65888-C4-2-P
dc.relation.projectID Gobierno de España. MTM2012-36732-C03-01
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 018
dc.identifier.publicationlastpage 43
dc.identifier.publicationtitle Symmetry Integrability and Geometry: Methods and Applications
dc.identifier.publicationvolume 14
dc.identifier.uxxi AR/0000026486
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.contributor.funder European Commission
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Análisis Aplicado
dc.type.hasVersion VoR
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