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Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
Christophe Charlier, Alfredo Deaño · 2017-08-08 · via math.PR updates on arXiv.org

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.

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