The hermitian two matrix model with an even quartic potential
2012 (English)In: Memoirs of the American Mathematical Society, ISSN 0065-9266, Vol. 217, no 1022, 1-118 p.Article in journal (Refereed) Published
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 Ã— 4 matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of M 1Â· Our results generalize earlier results for the case Î± = 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.
Correlation kernel, Eigenvalue distribution, Riemann-Hilbert problem, Steepest descent analysis, Two matrix model, Vector equilibrium problem
IdentifiersURN: urn:nbn:se:kth:diva-98506DOI: 10.1090/S0065-9266-2011-00639-8ISI: 000302510000001ScopusID: 2-s2.0-84859945063OAI: oai:DiVA.org:kth-98506DiVA: diva2:537927
QC 201206282012-06-282012-06-272012-06-28Bibliographically approved