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

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URI: https://hdl.handle.net/10016/32009
ISSN: 1815-0659
DOI: https://doi.org/10.3842/SIGMA.2018.018
UXXI: AR/0000026486
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asymptotics_SIGMA_2018.pdf (642.54 KB)
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2018-03-07
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Kiïv: Department of Applied Research Institute of Mathematics of National Academy of Science of Ukraine
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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 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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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
Keywords
Asymptotic analysis, Riemann-Hilbert problems, Hankel determinants, Random matrix theory, Painlevé equations
Bibliographic citation
SIGMA, (2018), v. 14, 018, [43] p.
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