عنوان

Orthogonal polynomials and random matrices: a Riemann-Hilbert approach

عنوان اصلي

Orthogonal polynomials and random matrices: a Riemann-Hilbert approach

محل نشرو پخش و غیره

Providence, R.I.

نام ناشر، پخش کننده و غيره

American Mathematical Society

تاریخ نشرو بخش و غیره

c2000

نام خاص و کميت اثر

ix, 261 p. : ill

ساير اطلاعات عنواني

Courant lecture notes in mathematics

ساير اطلاعات عنواني

3

متن يادداشت

Originally published: New York : Courant Institute of Mathematical Sciences, New York University, c1999

متن يادداشت

Includes bibliographical references )p.259-261(

متن يادداشت

Percy Deift

متن يادداشت

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 31 -- 2.1. Jacobi Matrices 31 -- 2.2. The Spectrum of Jacobi Matrices 32 -- 2.3. The Toda Flow 52 -- 2.4. Unbounded Jacobi Operators 62 -- 2.5. Appendix: Support of a Measure 53 -- Chapter 3. Orthogonal Polynomials 73 -- 3.1. Construction of Orthogonal Polynomials 73 -- 3.2. A Riemann-Hilbert Problem 34 -- 3.3. Some Symmetry Considerations 94 -- 3.4. Zeros of Orthogonal Polynomials 25 -- Chapter 4. Continued Fractions 75 -- 4.1. Continued Fraction Expansion of a Number 75 -- 4.2. Measure Theory and Ergodic Theory 46 -- 4.3. Application to Jacobi Operators 67 -- 4.4. Remarks on the Continued Fraction Expansion of a Number 58 -- Chapter 5. Random Matrix Theory 98 -- 5.1. Introduction 98 -- 5.2. Unitary Ensembles 19 -- 5.3. Spectral Variables for Hermitian Matrices 49 -- 5.4. Distribution of Eigenvalues 101 -- 5.5. Distribution of Spacings of Eigenvalues 311 -- 5.6. Further Remarks on the Nearest-Neighbor Spacing Distribution and -- Universality 021 -- Chapter 6. Equilibrium Measures 921 -- 6.1. Scaling 921 -- 6.2. Existence of the Equilibrium Measure LLV 431 -- 6.3. Convergence of X,* 541 -- 6.4. Convergence of RlI)xl(dxl 941 -- 6.5. Convergence of rlx* 951 -- 6.6. Variational Problem for the Equilibrium Measure 761 -- 6.7. Equilibrium Measure for V)x( = tx2m 961 -- 6.8. Appendix: The Transfinite Diameter and Fekete Sets 971 -- Chapter 7. Asymptotics for Orthogonal Polynomials 181 -- 7.1. Riemann-Hilbert Problem: The Precise Sense 181 -- 7.2. Riemann-Hilbert Problem for Orthogonal Polynomials 981 -- 7.3. Deformation of a Riemann-Hilbert Problem 191 -- 7.4. Asymptotics of Orthogonal Polynomials 102 -- 7.5. Some Analytic Considerations of Riemann-Hilbert Problems 802 -- 7.6. Construction of the Parametrix 312 -- 7.7. Asymptotics of Orthogonal Polynomials on the Real Axis 032 -- Chapter 8. Universality 732 -- 8.1. Universality 732 -- 8.2. Asymptotics of Ps 152

عنصر شناسه ای

، Orthogonal polynomials

عنصر شناسه ای

، Random matrices

شماره رده

تاريخ

5491-

عنصر شناسه اي

Deift, Percy

کد نقش

AU

عنصر شناسه اي

TI