عنوان

Orthogonal polynomials and random matrices: a Riemann-Hilbert approach

Title Proper

Orthogonal polynomials and random matrices: a Riemann-Hilbert approach

Place of Publication, Distribution, etc.

Providence, R.I.

Name of Publisher, Distributor, etc.

American Mathematical Society

Date of Publication, Distribution, etc.

c2000

Specific Material Designation and Extent of Item

ix, 261 p. : ill

Other Title Information

Courant lecture notes in mathematics

Other Title Information

3

Text of Note

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

Text of Note

Includes bibliographical references )p.259-261(

Text of Note

Percy Deift

Text of Note

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

Entry Element

، Orthogonal polynomials

Entry Element

، Random matrices

Class number

Dates

5491-

Entry Element

Deift, Percy

Relator Code

AU

TI