عنوان

Orthogonal polynomials and random matrices

(Number (ISBN

0821826956

Country Code

IR

Number

EB16131

.Language of Text, Soundtrack etc

انگلیسی

Country of publication

IR

Title Proper

Orthogonal polynomials and random matrices

General Material Designation

[Electronic Resource]

Other Title Information

:a Riemann-Hilbert approach

First Statement of Responsibility

/ Percy Deift

Place of Publication, Distribution, etc.

Providence, R.I.

Name of Publisher, Distributor, etc.

: American Mathematical Society,

Date of Publication, Distribution, etc.

, 2000.

Specific Material Designation and Extent of Item

ix, 261 p. ill. 26 cm.

Series Title

(Courant lecture notes in mathematics

Volume Designation

; 3)

Text of Note

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

Text of Note

e

Text of Note

ng

Text of Note

Includes bibliographical references (p. 259-261).

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 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.

Orthogonal polynomials

Random matrices

Number

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Book number

Deift, Percy,1945-

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ایران

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0821826956.djvu

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محرمانه

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محرمانه

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0821826956.djvu

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0

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old catalog

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