Universality limits for generalized Jacobi measures

Abstract

In this paper universality limits are studied in connection with measures which exhibit power-type singular behavior somewhere in their support. We extend the results of Lubinsky for Jacobi measures supported on $[-1,1]$ to generalized Jacobi measures supported on a compact subset of the real line, where the singularity can be located in the interior or at an endpoint of the support. The analysis is based upon the Riemann-Hilbert method, Christoffel functions, the polynomial inverse image method of Totik and the normal family approach of Lubinsky.

55 pages