TY  - BOOK
AU  - Duits,Maurice
AU  - Kuijlaars,Arno B.J.
AU  - Mo,Man Yue
TI  - Hermitian Two Matrix Model with an Even Quartic Potential
T2  - Memoirs of the American Mathematical Society
SN  - 9780821887561
AV  - QA379 -- .D858 2011eb 
U1  - 512.7/4 
PY  - 2012///
CY  - Providence
PB  - American Mathematical Society
KW  - Boundary value problems
KW  - Hermitian structures
KW  - Eigenvalues
KW  - Random matrices
KW  - Electronic books
N1  - Intro -- Contents -- Abstract -- Chapter 1. Introduction and Statement of Results -- 1.1. Hermitian two matrix model -- 1.2. Background -- 1.3. Vector equilibrium problem -- 1.4. Solution of vector equilibrium problem -- 1.5. Classification into cases -- 1.6. Limiting mean eigenvalue distribution -- 1.7. About the proof of Theorem 1.4 -- 1.8. Singular cases -- Chapter 2. Preliminaries and the Proof of Lemma 1.2 -- 2.1. Saddle point equation and functions sj -- 2.2. Values at the saddles and functions j -- 2.3. Large z asymptotics -- 2.4. Two special integrals -- 2.5. Proof of Lemma 1.2 -- Chapter 3. Proof of Theorem 1.1 -- 3.1. Results from potential theory -- 3.2. Equilibrium problem for 3 -- 3.3. Equilibrium problem for 1 -- 3.4. Equilibrium problem for 2 -- 3.5. Uniqueness of the minimizer -- 3.6. Existence of the minimizer -- 3.7. Proof of Theorem 1.1 -- Chapter 4. A Riemann Surface -- 4.1. The g-functions -- 4.2. Riemann surface R and -functions -- 4.3. Properties of the  functions -- 4.4. The  functions -- Chapter 5. Pearcey Integrals and the First Transformation -- 5.1. Definitions -- 5.2. Large z asymptotics -- 5.3. First transformation: Y X -- 5.4. RH problem for X -- Chapter 6. Second Transformation X U -- 6.1. Definition of second transformation -- 6.2. Asymptotic behavior of U -- 6.3. Jump matrices for U -- 6.4. RH problem for U -- Chapter 7. Opening of Lenses -- 7.1. Third transformation U T -- 7.2. RH problem for T -- 7.3. Jump matrices for T -- 7.4. Fourth transformation T S -- 7.5. RH problem for S -- 7.6. Behavior of jumps as n -- Chapter 8. Global Parametrix -- 8.1. Statement of RH problem -- 8.2. Riemann surface as an M-curve -- 8.3. Canonical homology basis -- 8.4. Meromorphic differentials -- 8.5. Definition and properties of functions uj -- 8.6. Definition and properties of functions vj -- 8.7. The first row of M; 8.8. The other rows of M -- Chapter 9. Local Parametrices and Final Transformation -- 9.1. Local parametrices -- 9.2. Final transformation -- 9.3. Proof of Theorem 1.4 -- Bibliography -- Index
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ER  -