Title: The Hermitian two matrix model with an even quartic potential
Authors: Duits, Maurice *
Kuijlaars, Arno * ×
Mo, Man Yue * #
Issue Date: 2012
Publisher: The Society
Series Title: Memoirs of the American Mathematical Society vol:217 issue:1022 pages:1-105
Abstract: We consider the two matrix model with an even quartic potential W(y)=y^4/4+ alpha y^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 x 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 alpha=0$, where the external field on the third measure was not present.
ISSN: 0065-9266
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
* (joint) first author
× corresponding author
# (joint) last author

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