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

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 obser...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Authors: Charlier, C., Deaño, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209446
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Asymptotics 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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Description
Summary: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.
ISSN:1815-0659