Strong asymptotics of orthogonal polynomials with respect to exponential weights

P. Deift, T. Kriecherbauer, Kenneth D T Mclaughlin, S. Venakides, X. Zhou

Research output: Contribution to journalArticle

324 Citations (Scopus)

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
StatePublished - Dec 1999

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Exponential Weights
Orthogonal Polynomials
Polynomials
Coefficient
Riemann-Hilbert Problem
Steepest Descent
Asymptotic Formula
Real Line
Recurrence
Argand diagram
Entire
Denote
Polynomial
Zero

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Strong asymptotics of orthogonal polynomials with respect to exponential weights. / Deift, P.; Kriecherbauer, T.; Mclaughlin, Kenneth D T; Venakides, S.; Zhou, X.

In: Communications on Pure and Applied Mathematics, Vol. 52, No. 12, 12.1999, p. 1491-1552.

Research output: Contribution to journalArticle

Deift, P. ; Kriecherbauer, T. ; Mclaughlin, Kenneth D T ; Venakides, S. ; Zhou, X. / Strong asymptotics of orthogonal polynomials with respect to exponential weights. In: Communications on Pure and Applied Mathematics. 1999 ; Vol. 52, No. 12. pp. 1491-1552.
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