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

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dc.contributor.authorCharlier, C.
dc.contributor.authorDeaño, A.
dc.date.accessioned2025-11-21T18:59:52Z
dc.date.issued2018
dc.description.abstractWe study n×n 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.sponsorshipC. 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 Competitiveness. 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.identifier.citationAsymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity / C. Charlier, A. Deaño // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2018.018
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 30E15; 35Q15; 15B52; 33E17
dc.identifier.otherarXiv: 1708.02519
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/209446
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleAsymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2018, том 14, випуск за цей рік