Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane

@inproceedings{Balogh2016OrthogonalPF,
  title={Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane},
  author={F. Balogh and Tamara Grava and D. Merzi},
  year={2016}
}
We obtain the strong asymptotics of polynomials pn(λ), λ ∈ C, orthogonal with respect to measures in the complex plane of the form e 2s−tλs−tλs)dA(λ), 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. We study the asymptotic behaviour of pn(λ) in the limit n,N → ∞ in such a way that n/N → T constant. Such asymptotic behaviour has two distinguished regimes according to the topology of… CONTINUE READING

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