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Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 14, article id 018Article in journal (Refereed) Published
Abstract [en]

We study n x 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 Painleve IV equation.

Place, publisher, year, edition, pages
NATL ACAD SCI UKRAINE, INST MATH , 2018. Vol. 14, article id 018
Keyword [en]
asymptotic analysis, Riemann-Hilbert problems, Hankel determinants, random matrix theory, Painleve equations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-225227DOI: 10.3842/SIGMA.2018.018ISI: 000427079500001Scopus ID: 2-s2.0-85045049285OAI: oai:DiVA.org:kth-225227DiVA, id: diva2:1194892
Note

QC 20180404

Available from: 2018-04-04 Created: 2018-04-04 Last updated: 2018-04-04Bibliographically approved

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