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Painlevé Kernels in Hermitian Matrix Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
2014 (English)In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940, Vol. 39, no 1, 173-196 p.Article in journal (Refereed) Published
Abstract [en]

After reviewing the Hermitian one-matrix model, we will give a brief introduction to the Hermitian two-matrix model and present a summary of some recent results on the asymptotic behavior of the two-matrix model with a quartic potential. In particular, we will discuss a limiting kernel in the quartic/quadratic case that is constructed out of a 4x4 Riemann-Hilbert problem related to the Painlev, II equation. Also an open problem will be presented.

Place, publisher, year, edition, pages
2014. Vol. 39, no 1, 173-196 p.
Keyword [en]
Hermitian matrix models, Eigenvalue distribution, Correlation kernel, Critical phenomena, Painleve transcendents, Biorthogonal polynomials, Riemann-Hilbert problems
National Category
URN: urn:nbn:se:kth:diva-140118DOI: 10.1007/s00365-013-9201-7ISI: 000328829600008ScopusID: 2-s2.0-84891016563OAI: diva2:690012
Knut and Alice Wallenberg Foundation, KAW 2010.0063

QC 20140122

Available from: 2014-01-22 Created: 2014-01-17 Last updated: 2014-01-22Bibliographically approved

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Duits, Maurice
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