Pollaczek multiple orthogonal polynomials ensembles

Analysis Seminar
Monday, June 2, 2014 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Alexander Aptekarev – Keldysh Institute, Russia
Jeff Geronimo
We discuss asymptotics of multiple orthogonal polynomials with respect to Nikishin systems generated by two measures (\sigma_1, \sigma_2) with unbounded supports (supp(\sigma_1) \subset \mathbb{R}_+, supp(\sigma_2) \subset \mathbb{R}_-); moreover, the second measure \sigma_2 is discrete. We focus on deriving the strong and weak asymptotic for a special system of multiple OP from this class with respect to two Pollaczek type weights on \mathbb{R}_+. The weak asymptotic for these polynomials can be obtained by means of solution of an equilibrium problem. For the strong asymptotic we use the matrix Riemann-Hilbert approach.