Strong asymptotics of orthogonal polynomials with respect to exponential weights

P. Deift, T. Kriecherbauer, K. T.R. Mclaughlin, S. Venakides, X. Zhou

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1491-1552
Number of pages62
JournalCommunications on Pure and Applied Mathematics
Volume52
Issue number12
DOIs
StatePublished - Dec 1999

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Strong asymptotics of orthogonal polynomials with respect to exponential weights'. Together they form a unique fingerprint.

  • Cite this