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a Riemann-Hilbert approach

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The cover of “Orthogonal polynomials and random matrices” - Open Library.

"Orthogonal polynomials and random matrices" was published by American Mathematical Society in 2000 - Providence, R.I, it has 261 pages and the language of the book is English.


“Orthogonal polynomials and random matrices” Metadata:

  • Title: ➤  Orthogonal polynomials and random matrices
  • Author:
  • Language: English
  • Number of Pages: 261
  • Publisher: American Mathematical Society
  • Publish Date:
  • Publish Location: Providence, R.I

“Orthogonal polynomials and random matrices” Subjects and Themes:

Edition Specifications:

  • Pagination: ix, 261 p. :

Edition Identifiers:

AI-generated Review of “Orthogonal polynomials and random matrices”:


"Orthogonal polynomials and random matrices" Table Of Contents:

  • 1- Machine generated contents note: Chapter 1. Riemann-Hilbert Problems 1
  • 2- 1.1. What Is a Riemann-Hilbert Problem? 1
  • 3- 1.2. Examples 4
  • 4- Chapter 2. Jacobi Operators 13
  • 5- 2.1. Jacobi Matrices 13
  • 6- 2.2. The Spectrum of Jacobi Matrices 23
  • 7- 2.3. The Toda Flow 25
  • 8- 2.4. Unbounded Jacobi Operators 26
  • 9- 2.5. Appendix: Support of a Measure 35
  • 10- Chapter 3. Orthogonal Polynomials 37
  • 11- 3.1. Construction of Orthogonal Polynomials 37
  • 12- 3.2. A Riemann-Hilbert Problem 43
  • 13- 3.3. Some Symmetry Considerations 49
  • 14- 3.4. Zeros of Orthogonal Polynomials 52
  • 15- Chapter 4. Continued Fractions 57
  • 16- 4.1. Continued Fraction Expansion of a Number 57
  • 17- 4.2. Measure Theory and Ergodic Theory 64
  • 18- 4.3. Application to Jacobi Operators 76
  • 19- 4.4. Remarks on the Continued Fraction Expansion of a Number 85
  • 20- Chapter 5. Random Matrix Theory 89
  • 21- 5.1. Introduction 89
  • 22- 5.2. Unitary Ensembles 91
  • 23- 5.3. Spectral Variables for Hermitian Matrices 94
  • 24- 5.4. Distribution of Eigenvalues 101
  • 25- 5.5. Distribution of Spacings of Eigenvalues 113
  • 26- 5.6. Further Remarks on the Nearest-Neighbor Spacing Distribution and
  • 27- Universality 120
  • 28- Chapter 6. Equilibrium Measures 129
  • 29- 6.1. Scaling 129
  • 30- 6.2. Existence of the Equilibrium Measure LLV 134
  • 31- 6.3. Convergence of X,* 145
  • 32- 6.4. Convergence of RlI(xl)dxl 149
  • 33- 6.5. Convergence of rlx* 159
  • 34- 6.6. Variational Problem for the Equilibrium Measure 167
  • 35- 6.7. Equilibrium Measure for V(x) = tx2m 169
  • 36- 6.8. Appendix: The Transfinite Diameter and Fekete Sets 179
  • 37- Chapter 7. Asymptotics for Orthogonal Polynomials 181
  • 38- 7.1. Riemann-Hilbert Problem: The Precise Sense 181
  • 39- 7.2. Riemann-Hilbert Problem for Orthogonal Polynomials 189
  • 40- 7.3. Deformation of a Riemann-Hilbert Problem 191
  • 41- 7.4. Asymptotics of Orthogonal Polynomials 201
  • 42- 7.5. Some Analytic Considerations of Riemann-Hilbert Problems 208
  • 43- 7.6. Construction of the Parametrix 213
  • 44- 7.7. Asymptotics of Orthogonal Polynomials on the Real Axis 230
  • 45- Chapter 8. Universality 237
  • 46- 8.1. Universality 237
  • 47- 8.2. Asymptotics of Ps 251.

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