Universality limits for generalized Jacobi measures

TL;DR

This paper extends universality limit results for Jacobi measures to generalized measures with power-type singularities on compact supports, using advanced analytical methods.

Contribution

It introduces new universality limits for generalized Jacobi measures with interior or endpoint singularities, expanding prior results to more general settings.

Findings

Universality limits are established for generalized Jacobi measures.

The results apply to measures with singularities inside or at the endpoints.

The analysis employs Riemann-Hilbert, Christoffel functions, and polynomial inverse image methods.

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.