Abstract
We consider polynomials orthogonal on [0,∞) with respect to Laguerre-type weights w(x) = xα e-Q(x), where α > -1 and where Q denotes a polynomial with positive leading coefficient. The main purpose of this paper is to determine Plancherel-Rotach-type asymptotics in the entire complex plane for the orthonormal polynomials with respect to w, as well as asymptotics of the corresponding recurrence coefficients and of the leading coefficients of the orthonormal polynomials. As an application we will use these asymptotics to prove universality results in random matrix theory. We will prove our results by using the characterization of orthogonal polynomials via a 2 × 2 matrix valued Riemann--Hilbert problem, due to Fokas, Its, and Kitaev, together with an application of the Deift-Zhou steepest descent method to analyze the Riemann-Hilbert problem asymptotically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vanlessen, M. Strong Asymptotics of Laguerre-Type Orthogonal Polynomials and Applications in Random Matrix Theory. Constr Approx 25, 125–175 (2007). https://doi.org/10.1007/s00365-005-0611-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00365-005-0611-z