Strong asymptotics of orthogonal polynomials with respect to exponential weights

Published

Journal Article

We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e-Q(x)dx on the real line, where Q(x) = Σ2mk=0qkxk, q2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem following [22, 23]. We employ the steepest-descent-type method introduced in [18] and further developed in [17, 19] in order to obtain uniform Plancherel-Rotach-type asymptotics in the entire complex plane, as well as asymptotic formulae for the zeros, the leading coefficients, and the recurrence coefficients of the orthogonal polynomials. © 1999 John Wiley & Sons, Inc.

Full Text

Duke Authors

Cited Authors

  • Deift, P; Kriecherbauer, T; Mclaughlin, KTR; Venakides, S; Zhou, X

Published Date

  • January 1, 1999

Published In

Volume / Issue

  • 52 / 12

Start / End Page

  • 1491 - 1552

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/(SICI)1097-0312(199912)52:12<1491::AID-CPA2>3.0.CO;2-#

Citation Source

  • Scopus