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

Charlier, Christophe, Deaño, Alfredo (2018) Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity. Symmetry, Integrability and Geometry: Methods and Applications, 14 . Article Number 18. ISSN 1815-0659. (doi:10.3842/SIGMA.2018.018) (KAR id:66333)

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https://doi.org/10.3842/SIGMA.2018.018

Abstract

We 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.

Item Type: Article
DOI/Identification number: 10.3842/SIGMA.2018.018
Uncontrolled keywords: asymptotic analysis; Riemann–Hilbert problems; Hankel determinants; random matrix theory; Painleve equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Alfredo Deano Cabrera
Date Deposited: 09 Mar 2018 12:45 UTC
Last Modified: 16 Feb 2021 13:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/66333 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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