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

Charlier, Christophe; Deaño Cabrera, Alfredo

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

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Análisis Aplicado	es
dc.contributor.author	Charlier, Christophe
dc.contributor.author	Deaño Cabrera, Alfredo
dc.contributor.funder	Ministerio de Economía y Competitividad (España)	es
dc.contributor.funder	European Commission	en
dc.date.accessioned	2021-02-24T09:55:44Z
dc.date.available	2021-02-24T09:55:44Z
dc.date.issued	2018-03-07
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	en
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.	en
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.	en
dc.description.status	Publicado	es
dc.format.extent	43
dc.identifier.bibliographicCitation	SIGMA, (2018), v. 14, 018, [43] p.	en
dc.identifier.doi	https://doi.org/10.3842/SIGMA.2018.018
dc.identifier.issn	1815-0659
dc.identifier.publicationfirstpage	1
dc.identifier.publicationissue	018
dc.identifier.publicationlastpage	43	es
dc.identifier.publicationtitle	Symmetry Integrability and Geometry: Methods and Applications	en
dc.identifier.publicationvolume	14
dc.identifier.uri	https://hdl.handle.net/10016/32009
dc.identifier.uxxi	AR/0000026486
dc.language.iso	eng	en
dc.publisher	Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine	en
dc.relation.projectID	info:eu-repo/grantAgreement/EC/FP7-ERC-307074	es
dc.relation.projectID	Gobierno de España. MTM2015-65888-C4-2-P	es
dc.relation.projectID	Gobierno de España. MTM2012-36732-C03-01	es
dc.rights	The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License.	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Matemáticas	es
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Riemann-Hilbert problems	en
dc.subject.other	Hankel determinants	en
dc.subject.other	Random matrix theory	en
dc.subject.other	Painlevé equations	en
dc.title	Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity	en
dc.type	research article	*
dc.type.hasVersion	VoR	*
dspace.entity.type	Publication