Universality Limits involving Orthogonal Polynomials on an Arc of the Unit Circle

We establish universality limits for measures on a subarc of the unit circle. Assume that mu is a regular measure on such an arc, in the sense of Stahl, Totik, and Ullmann, and is absolutely continuous in an open arc containing some point . Assume, moreover, that is positive and continuous at z(0). Then universality for mu holds at z(0), in the sense that the reproducing kernel K-n (z,t) for mu satisfies lim(n ->infinity) K-n(z(0) exp(2 pi is/n), z(0) exp(2 pi i (t) over bar /n))/K-n (z(0), z(0)) = e(i pi(s-t))S((s-t)T(theta(0))), uniformly for s,t in compact subsets of the plane, where S(z) = sin pi z/pi z is the sinc kernel, and T/2 pi is the equilibrium density for the arc.