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The hermitian two matrix model with an even quartic potential
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7598-4521
2012 (English)In: Memoirs of the American Mathematical Society, ISSN 0065-9266, E-ISSN 1947-6221, Vol. 217, no 1022, 1-118 p.Article in journal (Refereed) Published
Abstract [en]

We consider the two matrix model with an even quartic potential W(y) = y 4/4+ ay 2/2 and an even polynomial potential V(x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices M 1. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a 4 × 4 matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of M 1· Our results generalize earlier results for the case α = 0, where the external field on the third measure was not present.

Place, publisher, year, edition, pages
2012. Vol. 217, no 1022, 1-118 p.
Keyword [en]
Correlation kernel, Eigenvalue distribution, Riemann-Hilbert problem, Steepest descent analysis, Two matrix model, Vector equilibrium problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-98506DOI: 10.1090/S0065-9266-2011-00639-8ISI: 000302510000001Scopus ID: 2-s2.0-84859945063OAI: oai:DiVA.org:kth-98506DiVA: diva2:537927
Note
QC 20120628Available from: 2012-06-28 Created: 2012-06-27 Last updated: 2017-12-07Bibliographically approved

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Duits, Maurice

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