Memoirs of the American Mathematical Society 2012; 105 pp; softcover Volume: 217 ISBN10: 0821869280 ISBN13: 9780821869284 List Price: US$70 Individual Members: US$42 Institutional Members: US$56 Order Code: MEMO/217/1022
 The authors 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 \(4\times4\) matrix valued RiemannHilbert problem that characterizes the correlation kernel for the eigenvalues of \(M_1\). The authors' results generalize earlier results for the case \(\alpha=0\), where the external field on the third measure was not present. Table of Contents  Introduction and statement of results
 Preliminaries and the proof of Lemma 1.2
 Proof of Theorem 1.1
 A Riemann surface
 Pearcey integrals and the first transformation
 Second transformation \(X\mapsto U\)
 Opening of lenses
 Global parametrix
 Local parametrices and final transformation
 Bibliography
 Index
