Details

Autor(en) / Beteiligte

• Baik, J
• Kriecherbauer, T
• McLaughlin, K. T.-R
• Miller, P. D

Titel

Discrete orthogonal polynomials: asymptotics and applications (Annals of mathematics studies, number 164)

Auflage

1

Ort / Verlag

Princeton: Princeton University Press

Erscheinungsjahr

2007

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books,Discrete Orthogonal Polynomialsaddresses 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.