04187nam 2200649 450 991078861800332120170822144452.00-8218-8756-4(CKB)3360000000464082(EBL)3114563(SSID)ssj0000726486(PQKBManifestationID)11441186(PQKBTitleCode)TC0000726486(PQKBWorkID)10683097(PQKB)10812249(MiAaPQ)EBC3114563(RPAM)17137832(PPN)195419111(EXLCZ)99336000000046408220150416h20112011 uy 0engur|n|---|||||txtccrThe Hermitian two matrix model with an even quartic potential /Maurice Duits, Arno B.J. Kuijlaars, Man Yue MoProvidence, Rhode Island :American Mathematical Society,2011.©20111 online resource (105 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 217, Number 1022"May 2012, Volume 217, Number 1022 (end of volume)."0-8218-6928-0 Includes bibliographical references and index.""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""Memoirs of the American Mathematical Society ;Volume 217, Number 1022.Boundary value problemsHermitian structuresEigenvaluesRandom matricesBoundary value problems.Hermitian structures.Eigenvalues.Random matrices.512.7/4Duits Maurice1542993Kuijlaars Arno B. J.1963-Mo Man YueMiAaPQMiAaPQMiAaPQBOOK9910788618003321The Hermitian two matrix model with an even quartic potential3796227UNINA