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

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

Author(s): Charlier, Christophe; Deaño Cabrera, Alfredo
Publisher: Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine
Issued date: 2018-03-07
Citation: SIGMA, (2018), v. 14, 018, [43] p.
ISSN: 1815-0659
DOI: https://doi.org/10.3842/SIGMA.2018.018
xmlui.dri2xhtml.METS-1.0.item-contributor-funder: Ministerio de Economía y Competitividad (España)
European Commission
Sponsor: 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.
Project: info:eu-repo/grantAgreement/EC/FP7-ERC-307074
Gobierno de España. MTM2015-65888-C4-2-P
Gobierno de España. MTM2012-36732-C03-01
Keywords: Asymptotic analysis , Riemann-Hilbert problems , Hankel determinants , Random matrix theory , Painlevé equations
URI: http://hdl.handle.net/10016/32009
Rights: The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License.
Atribución-NoComercial-SinDerivadas 3.0 España
The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License.

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 [+]

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

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