On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Bertola, M., Tovbis, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148547
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight / M. Bertola, A. Tovbis // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ.

We study the asymptotics of recurrence coefficients for monic orthogonal polynomials πn(z) with the quartic exponential weight exp[−N(1/2z²+1/4tz⁴)], where t∈C and N∈N, N→∞. Our goal is to describe these asymptotic behaviors globally for t∈C in different regions. We also describe the ''bre...