We discuss probability measures arising as weak* limits of normalized counting measures on the Galois conjugates of algebraic integers. Given a compact set in the complex plane, symmetric with respect to the real axis, such measures are recently characterized by Alex Smith. However, not many explicit examples of measures satisfying this characterization are known.
In this talk, we give a dense class of examples of probability measures on the given set that can occur in this way. In particular, we study measures on interval with integer endpoints. Our approach uses techniques from logarithmic potential theory.
