Discrete Orthogonal Polynomials
Asymptotics and Applications
1st Edition
Published on 2. January 2007
184 pages
978-1-4008-3713-7 (ISBN)
Description
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.
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.
More details
Edition
Course Book
Language
English
Place of publication
Princeton, NJ
United States
Publishing group
De Gruyter
Target group
Professional and scholarly
Edition type
Digital original
Illustrations
14 halftones. 6 line illus.
File size
2,57 MB
ISBN-13
978-1-4008-3713-7 (9781400837137)
Schweitzer Classification
Other editions
Additional editions
J. Baik | T. Kriecherbauer | Kenneth Dean T-R McLaughlin
Discrete Orthogonal Polynomials
Asymptotics and Applications
Book
01/2007
Princeton University Press
€59.10
Article not available at the moment
J. Baik | T. Kriecherbauer | Kenneth D.T-R McLaughlin
Discrete Orthogonal Polynomials
Asymptotics and Applications
Book
01/2007
Princeton University Press
€84.18
Article exhausted; check different version
Persons
J. Baik is Associate Professor of Mathematics at the University of Michigan. T. Kriecherbauer is Professor of Mathematics at Ruhr-Universität Bochum in Bochum, Germany. K. T.-R. McLaughlin is Professor of Mathematics at the University of Arizona. P. D. Miller is Associate Professor of Mathematics at the University of Michigan.
Content
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
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
