LEADER 04189nam 2200649 450 001 9910479996103321 005 20170822144452.0 010 $a0-8218-8756-4 035 $a(CKB)3360000000464082 035 $a(EBL)3114563 035 $a(SSID)ssj0000726486 035 $a(PQKBManifestationID)11441186 035 $a(PQKBTitleCode)TC0000726486 035 $a(PQKBWorkID)10683097 035 $a(PQKB)10812249 035 $a(MiAaPQ)EBC3114563 035 $a(PPN)195419111 035 $a(EXLCZ)993360000000464082 100 $a20150416h20112011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Hermitian two matrix model with an even quartic potential /$fMaurice Duits, Arno B.J. Kuijlaars, Man Yue Mo 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2011. 210 4$dİ2011 215 $a1 online resource (105 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 217, Number 1022 300 $a"May 2012, Volume 217, Number 1022 (end of volume)." 311 $a0-8218-6928-0 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""8.3. Canonical homology basis""""8.4. Meromorphic differentials""; ""8.5. Definition and properties of functions uj""; ""8.6. Definition and properties of functions vj""; ""8.7. The first row of M""; ""8.8. The other rows of M""; ""Chapter 9. Local Parametrices and Final Transformation""; ""9.1. Local parametrices""; ""9.2. Final transformation""; ""9.3. Proof of Theorem 1.4""; ""Bibliography""; ""Index"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 217, Number 1022. 606 $aBoundary value problems 606 $aHermitian structures 606 $aEigenvalues 606 $aRandom matrices 608 $aElectronic books. 615 0$aBoundary value problems. 615 0$aHermitian structures. 615 0$aEigenvalues. 615 0$aRandom matrices. 676 $a512.7/4 700 $aDuits$b Maurice$0964789 702 $aKuijlaars$b Arno B. J.$f1963- 702 $aMo$b Man Yue 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910479996103321 996 $aThe Hermitian two matrix model with an even quartic potential$92188952 997 $aUNINA