Strong asymptotics for the Pollaczek multiple orthogonal polynomials ensembles

Abstract

We study the asymptotic properties of a class of multiple orthogonal polynomials with respect to a Nikishin system generated by two measures $({\sigma }_1,{\sigma }_2)$ with unbounded supports ($supp({\sigma }_1)\subset {\mathbb{R}}_{+}$, $supp({\sigma }_2)\subset {\mathbb{R}}_{-}$), and such that the second measure ${\sigma }_2$ is discrete. The weak asymptotics for these polynomials was obtained previously by V. Sorokin. We use his result and the Riemann-Hilbert analysis to derive the strong asymptotics of these polynomials and of the reproducing kernel.

38 pages, 7 figures

References in corpus (1)

• Nikishin systems are perfect. Case of unbounded and touching supports