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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 018, 43 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.018 (Mi sigma1317) 		 
This article is cited in 9 scientific papers (total in 9 papers)

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

Christophe Charliera, Alfredo Deañob

a Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, SE-114 28 Stockholm, Sweden
b School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7FS, UK
Full-text PDF (679 kB) Citations (9)
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DOI: https://doi.org/10.3842/SIGMA.2018.018
Abstract: 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.
Keywords: asymptotic analysis; Riemann–Hilbert problems; Hankel determinants; random matrix theory; Painlevé equations.
Funding agency Grant number
European Research Council 307074
Ministerio de Economía y Competitividad MTM2012-36732-C03-01
MTM2015-65888-C4-2-P
C. Charlier was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007/2013) / ERC Grant Agreement n. 307074. A. Deaño acknowledges financial support from projects MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P from the Spanish Ministry of Economy and Competitivity.
Received: November 2, 2017; in final form February 27, 2018; Published online March 7, 2018
Bibliographic databases:
Document Type: Article
MSC: 30E15; 35Q15; 15B52; 33E17
Language: English
Citation: Christophe Charlier, Alfredo Deaño, “Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity”, SIGMA, 14 (2018), 018, 43 pp.
Citation in format AMSBIB
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\paper Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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