Description 
1 online resource (v, 144 pages) 
Series 
Memoirs of the American Mathematical Society ; number 1289 

Memoirs of the American Mathematical Society ; no. 1289

Contents 
Cover  Title page  Chapter 1. Introduction  Chapter 2. Statement of main results  2.1. Phase diagram of the cubic model  2.2. The limiting boundary of eigenvalues as a polynomial curve  2.3. Spectral curve  2.4. Phase transition of the spectral curve  2.5. The parameters (, ₀) as a change of variables  2.6. The mother body problem  2.7. Associated multiple orthogonality  2.8. Behavior at the boundary of the phase diagram  2.9. The Sproperty  2.10. Statement of Results  ₁<0  2.11. Phase transition along the mother body critical curve 

2.12. Setup for the remainder of the paper  Chapter 3. Limiting boundary of eigenvalues. Proofs of Propositions 2.1 and 2.7 and Theorems 2.2, 2.5 and 2.8  3.1. Proof of Proposition 2.1  3.2. Proofs of Theorems 2.2, 2.5 and 2.8 and Proposition 2.7  Chapter 4. Geometry of the spectral curve. Proof of Theorem 2.6  4.1. The spectral curve for ₁=0  4.2. The spectral curve for ₁>0. Proof of Theorem 4.1  4.3. Sheet structure for ℛ  Chapter 5. Meromorphic quadratic differential on ℛ  5.1. Technical computations for the threecut case 

5.2. Technical computations for the onecut case  5.3. Quadratic differential on the spectral curve: general principles  5.4. Critical graph in the threecut case  5.5. Critical graph in the onecut case  Chapter 6. Proofs of Theorems 2.3, 2.4, 2.9 and 2.10  Chapter 7. RiemannHilbert analysis in the threecut case  7.1. Multiple orthogonality in terms of Airy functions  7.2. The RiemannHilbert problem  7.3. First transformation: \mapsto  7.4. Second transformation: \mapsto  7.5. Opening of lenses: \mapsto  7.6. The global parametrix  7.7. The local parametrices 

7.8. Final transformation: \mapsto  Chapter 8. RiemannHilbert analysis in the onecut case  Chapter 9. Construction of the global parametrix  9.1. The inverse of the rational parametrization  9.2. Construction of the global parametrix in the threecut case  9.3. Construction of the global parametrix in the onecut case  9.4. Explicit construction of the first row  Chapter 10. Proofs of Theorems 2.14 and 2.15  Appendix A. Analysis of the width parameters  A.1. Width parameters in the threecut case  A.2. Width parameters in the onecut case  Acknowledgements 
Summary 
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this present paper the authors consider the normal matrix model with cubic plus linear potential. In order to regularize the model, they follow Elbau & Felder and introduce a cutoff. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain \Omega that they determine explicitly by finding the rational parametrization of its bo 
Notes 
"May 2020, volume 265, number 1289 (sixth of 7 numbers)." 
Bibliography 
Includes bibliographical references 
Subject 
Matrices  Norms  Models


Functions of a complex variable {For analysis on manifolds, see 58XX}  Geometric function theory  None of the above, but in this section.


Functions of a complex variable {For analysis on manifolds, see 58XX}  Miscellaneous topics of analysis in the complex domain.


Functions of a complex variable {For analysis on manifolds, see 58XX}  Riemann surfaces  Differentials on Riemann surfaces.


Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For.


Potential theory {For probabilistic potential theory, see 60J45}  Twodimensional theory  Potentials and capacity, harmonic measure, extremal length [See also 30C85].


Probability theory and stochastic processes {For additional applications, see 11Kxx, 62XX, 90XX, 91XX, 92XX, 93XX, 94XX}  Probability theory on algebraic and topological structures  Random m.

Form 
Electronic book

Author 
Silva, Guilherme L. F., author.

ISBN 
1470461463 

9781470461461 
