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Discrete Orthogonal Polynomials: Asymptotics and Applications (Annals of Mathematics Studies)

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Synopses & Reviews

Publisher Comments:

This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case.

J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin and P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.

Synopsis:

This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case.

J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin and P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.

Synopsis:

This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case.

J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.

Table of Contents

Preface vii

Chapter 1. Introduction 1

Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane 25

Chapter 3. Applications 49

Chapter 4. An Equivalent Riemann-Hilbert Problem 67

Chapter 5. Asymptotic Analysis 87

Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in x2.3 105

Chapter 7. Universality: Proofs of Theorems Stated in x3.3 115

Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 135

Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 145

Appendix C. List of Important Symbols 153

Bibliography 163

Index 167

Product Details

ISBN:
9780691127347
Author:
Baik, J.
Publisher:
Princeton University Press
Author:
McLaughlin, Kenneth
Author:
Miller, Peter D.
Author:
Kriecherbauer, T.
Author:
McLaughlin, K. T. -R
Author:
McLaughlin, Kenneth D.T-R
Location:
Princeton
Subject:
Calculus
Subject:
Asymptotic theory
Subject:
Orthogonal polynomials.
Subject:
Discrete Mathematics
Subject:
Mathematics
Subject:
Orthogonal polynomials -- Asymptotic theory.
Subject:
Mathematics-Calculus
Copyright:
Edition Description:
Trade paper
Series:
Annals of Mathematics Studies
Publication Date:
January 2007
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
14 halftones. 6 line illus.
Pages:
184
Dimensions:
10 x 8 in

Related Subjects

History and Social Science » Politics » General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General

Discrete Orthogonal Polynomials: Asymptotics and Applications (Annals of Mathematics Studies) New Trade Paper
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Product details 184 pages Princeton University Press - English 9780691127347 Reviews:
"Synopsis" by , This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case.

J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin and P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.

"Synopsis" by , This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case.

J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.

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