Duits, Maurice and Kuijlaars, Arno B. J. and Mo, Man Yue (2012) The Hermitian two matrix model with an even quartic potential. Memoirs of the American Mathematical Society. Vol.217. No.1022. American Mathematical Society , Providence, Rhode Island. ISBN 9780821869284 http://resolver.caltech.edu/CaltechAUTHORS:20120507145446892

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Abstract
We consider the two matrix model with an even quartic potential W(y) = y^4/4 + αy^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 RiemannHilbert 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.
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Additional Information:  © 2011 American Mathematical Society. Received by editor(s): October 20, 2010; Posted: September 20, 2011. M. Duits and A.B.J. Kuijlaars are grateful for the support and hospitality of MSRI in Berkeley in the fall of 2010. A.B.J. Kuijlaars is supported by K.U. Leuven research grant OT/08/33, FWOFlanders project G.0427.09 and G.0641.11, by the Belgian Interuniversity Attraction Pole P06/02, and by grant MTM200806689C0201 of the Spanish Ministry of Science and Innovation. M. Y. Mo acknowledges financial support by the EPSRC grant EP/G019843/1.  
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Subject Keywords:  Two matrix model, eigenvalue distribution, correlation kernel, vector equilibrium problem, RiemannHilbert problem, steepest descent analysis  
Classification Code:  MSC (2010): Primary 30E25, 60B20; Secondary 15B52, 30F10, 31A05, 42C05, 82B26  
Record Number:  CaltechAUTHORS:20120507145446892  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20120507145446892  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  31339  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  08 May 2012 18:23  
Last Modified:  26 Dec 2012 15:10 
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