Discrete Orthogonal Polynomials
eBook - PDF

Discrete Orthogonal Polynomials

Asymptotics and Applications

  1. 184 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Discrete Orthogonal Polynomials

Asymptotics and Applications

About this book

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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Yes, you can access Discrete Orthogonal Polynomials by J. Baik,T. Kriecherbauer,Kenneth D.T-R McLaughlin,Peter D. Miller,Kenneth Dean T-R McLaughlin in PDF and/or ePUB format, as well as other popular books in Mathematics & Discrete Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1. Introduction
  7. Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane
  8. Chapter 3. Applications
  9. Chapter 4. An Equivalent Riemann-Hilbert Problem
  10. Chapter 5. Asymptotic Analysis
  11. Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3
  12. Chapter 7. Universality: Proofs of Theorems Stated in §3.3
  13. Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1
  14. Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17
  15. Appendix C. List of Important Symbols
  16. Bibliography
  17. Index