Zero distribution of orthogonal polynomials on a $q$-lattice

We give the asymptotic behavior of the zeros of orthogonal polynomials, after appropriate scaling, for which the orthogonality measure is supported on the $q$-lattice $\{q^k,\,k=0,1,2,3,\ldots\}$, where $0<q<1$. The asymptotic distribution of the zeros is given by the radial part of the equilibrium measure of an extremal problem in logarithmic potential theory for circular symmetric measures with a constraint imposed by the $q$-lattice. This is joint work with Quinten Van Baelen.