Discrete Orthogonal Polynomials. (AM-164) : : Asymptotics and Applications (AM-164) / / Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Baik, J.,; Kriecherbauer, T.,; McLaughlin, Kenneth D.T-R,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2007]; ©2007
• Year of Publication: 2007
• Edition: Course Book
• Language: English
• Series: Annals of Mathematics Studies ; 164
• Physical Description: 1 online resource (184 p.) :; 14 halftones. 6 line illus.
• Other title: Frontmatter --; Contents --; Preface --; Chapter 1. Introduction --; Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane --; Chapter 3. Applications --; Chapter 4. An Equivalent Riemann-Hilbert Problem --; Chapter 5. Asymptotic Analysis --; Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in §2.3 --; Chapter 7. Universality: Proofs of Theorems Stated in §3.3 --; Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 --; Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 --; Appendix C. List of Important Symbols --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400837137; 9783110494914; 9783110442502
• DOI: 10.1515/9781400837137
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Kenneth D.T-R McLaughlin, Peter D. Miller, T. Kriecherbauer, J. Baik.

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.