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

Symmetry Integrability and Geometry-Methods and Applications

article

Christophe Charlier¹  Alfredo Deaño² 

[1] Department of Mathematics, KTH Royal Institute of Technology;School of Mathematics, Statistics and Actuarial Science, University of Kent

关键词: asymptotic analysis;    Riemann–Hilbert problems;    Hankel determinants;    random matrix theory;    Painlev´e equations;   

DOI  :  10.3842/SIGMA.2018.018

来源: National Academy of Science of Ukraine

【 摘 要 】

We study $n\times n$ 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.

【 授权许可】

Unknown