An edition of Orthogonal polynomials and random matrices
(1999)
Orthogonal polynomials and random matrices
a Riemann-Hilbert approach
by Percy Deift
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April 28, 2010 | History
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Random matrices, Orthogonal polynomialsShowing 2 featured editions. View all 2 editions?
| Edition | Availability |
|---|---|
1
Orthogonal polynomials and random matrices: a Riemann-Hilbert approach
2000, American Mathematical Society
in English
0821826956 9780821826959
|
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2
Orthogonal polynomials and random matrices: a Riemann-Hilbert approach
1999, Courant Institute of Mathematical Sciences, New York University
in English
0965870324 9780965870320
|
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Libraries near you:
WorldCat
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Book Details
Table of Contents
Machine generated contents note: Chapter 1. Riemann-Hilbert Problems 1
1.1. What Is a Riemann-Hilbert Problem? 1
1.2. Examples 4
Chapter 2. Jacobi Operators 13
2.1. Jacobi Matrices 13
2.2. The Spectrum of Jacobi Matrices 23
2.3. The Toda Flow 25
2.4. Unbounded Jacobi Operators 26
2.5. Appendix: Support of a Measure 35
Chapter 3. Orthogonal Polynomials 37
3.1. Construction of Orthogonal Polynomials 37
3.2. A Riemann-Hilbert Problem 43
3.3. Some Symmetry Considerations 49
3.4. Zeros of Orthogonal Polynomials 52
Chapter 4. Continued Fractions 57
4.1. Continued Fraction Expansion of a Number 57
4.2. Measure Theory and Ergodic Theory 64
4.3. Application to Jacobi Operators 76
4.4. Remarks on the Continued Fraction Expansion of a Number 85
Chapter 5. Random Matrix Theory 89
5.1. Introduction 89
5.2. Unitary Ensembles 91
5.3. Spectral Variables for Hermitian Matrices 94
5.4. Distribution of Eigenvalues 101
5.5. Distribution of Spacings of Eigenvalues 113
5.6. Further Remarks on the Nearest-Neighbor Spacing Distribution and
Universality 120
Chapter 6. Equilibrium Measures 129
6.1. Scaling 129
6.2. Existence of the Equilibrium Measure LLV 134
6.3. Convergence of X,* 145
6.4. Convergence of RlI(xl)dxl 149
6.5. Convergence of rlx* 159
6.6. Variational Problem for the Equilibrium Measure 167
6.7. Equilibrium Measure for V(x) = tx2m 169
6.8. Appendix: The Transfinite Diameter and Fekete Sets 179
Chapter 7. Asymptotics for Orthogonal Polynomials 181
7.1. Riemann-Hilbert Problem: The Precise Sense 181
7.2. Riemann-Hilbert Problem for Orthogonal Polynomials 189
7.3. Deformation of a Riemann-Hilbert Problem 191
7.4. Asymptotics of Orthogonal Polynomials 201
7.5. Some Analytic Considerations of Riemann-Hilbert Problems 208
7.6. Construction of the Parametrix 213
7.7. Asymptotics of Orthogonal Polynomials on the Real Axis 230
Chapter 8. Universality 237
8.1. Universality 237
8.2. Asymptotics of Ps 251.
Edition Notes
Includes bibliographical references (p. 259-261).
Originally published: New York : Courant Institute of Mathematical Sciences, New York University, c1999.
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| April 28, 2010 | Edited by Open Library Bot | Linked existing covers to the work. |
| February 2, 2010 | Edited by WorkBot | add more information to works |
| December 9, 2009 | Created by WorkBot | add works page |