%0 Journal Article
%T Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane
%A Ferenc Balogh
%A Tamara Grava
%A Dario Merzi
%J Mathematics
%D 2015
%I arXiv
%X The purpose of this paper is to describe the strong asymptotics of orthogonal polynomials with respect to measures of the form $$ e^{-|z|^{2s}+tz^s+\overline{tz}^s}dA(z) $$ in the complex plane where $s$ is a positive integer, $t$ is a complex parameter and $dA$ stands for the area measure in the plane. Such problem has its origin from normal matrix models. After a natural symmetry reduction it is shown that the orthogonality conditions for the resulting polynomials on the complex plane can be written equivalently in terms of non-hermitian contour integral orthogonality conditions. The strong asymptotics for the orthogonal polynomials is obtained from the corresponding Riemann-Hilbert problem by using the Deift-Zhou nonlinear steepest descent method.
%U http://arxiv.org/abs/1509.05331v1