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The Hermitian two matrix model with an even quartic potential / / Maurice Duits, Arno B.J. Kuijlaars, Man Yue Mo
| The Hermitian two matrix model with an even quartic potential / / Maurice Duits, Arno B.J. Kuijlaars, Man Yue Mo |
| Autore | Duits Maurice |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina | 512.7/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Boundary value problems
Hermitian structures Eigenvalues Random matrices |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-8756-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Record Nr. | UNINA-9910479996103321 |
Duits Maurice
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Hermitian two matrix model with an even quartic potential / / Maurice Duits, Arno B.J. Kuijlaars, Man Yue Mo
| The Hermitian two matrix model with an even quartic potential / / Maurice Duits, Arno B.J. Kuijlaars, Man Yue Mo |
| Autore | Duits Maurice |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina | 512.7/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Boundary value problems
Hermitian structures Eigenvalues Random matrices |
| ISBN | 0-8218-8756-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Record Nr. | UNINA-9910788618003321 |
|
Duits Maurice
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Hermitian two matrix model with an even quartic potential / / Maurice Duits, Arno B.J. Kuijlaars, Man Yue Mo
| The Hermitian two matrix model with an even quartic potential / / Maurice Duits, Arno B.J. Kuijlaars, Man Yue Mo |
| Autore | Duits Maurice |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (105 p.) |
| Disciplina | 512.7/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Boundary value problems
Hermitian structures Eigenvalues Random matrices |
| ISBN | 0-8218-8756-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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"" |
| Record Nr. | UNINA-9910828788403321 |
|
Duits Maurice
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||