Journal
STUDIES IN APPLIED MATHEMATICS
Volume 122, Issue 1, Pages 29-83Publisher
WILEY
DOI: 10.1111/j.1467-9590.2008.00423.x
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Funding
- K.U. Leuven research [OT/04/21, OT/08/33]
- Belgian Interuniversity Attraction Pole [P06/02]
- FWO-Flanders [G.0455.04]
- European Science Foundation Program MISGAM
- Ministry of Education and Science of Spain [MTM2005-08648-C02-01]
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We study polynomials that are orthogonal with respect to the modified Laguerre weight z(-n+nu)e(-Nz)(z - 1)(2b), in the limit wheren, N -> infinity with N/n -> 1 and nu is a fixed number in R/N0.. With the effect of the factor (z - 1)(2b), the local parametrix near the critical point z = 1 can be constructed in terms of Psi functions associated with the PainlevE IV equation. We show that the asymptotics of the recurrence coefficients of orthogonal polynomials can be described in terms of specified solution of the PainlevE IV equation in the double scaling limit. Our method is based on the Deift/Zhou steepest decent analysis of the Riemann-Hilbert problem associated with orthogonal polynomials.
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