Strong asymptotics for the Pollaczek multiple orthogonal polynomials ensembles

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.