Discrete Orthogonal Polynomials. (AM-164)

"This volume is a well written contribution to the theory of asymptotics of discrete orthogonal polynomials and its applications."--H.J. Glaeske, Zentralblatt MATH "The book includes the authors' own research results developed over the last years. Their approach and proofs are straightforward constructive making this monograph accessible and valuable to undergraduate and graduate students, PhD students and researchers involved in the asymptotic analysis of systems of discrete orthogonal polynomials."--Octavian Agratini, Mathematica "This book is very interesting. It pulls together several methods developed during the last twenty years and makes them into a general theory. Thanks to this general theory, several open problems are solved. The organization of the book is very nice."--Sylvie Corteel, Mathematical Reviews

J. Baik is Associate Professor of Mathematics at the University of Michigan. T. Kriecherbauer is Professor of Mathematics at Ruhr-Universitat 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.

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