Asymptotics of r-fold symmetric multiple orthogonal polynomials

At the centre of this talk are polynomials on a single variable satisfying higher order recurrence relations with all recurrence coefficients, except the last one, equal to zero. The polynomials at issue are orthogonal with respect to a vector of measures, are rotational invariant and all the zeros lie on a star in the complex plane. The focus will be on the case where the recurrence coefficients are asymptotically periodic and unbounded, with an example of a Nikishin system to be detailed. The main points to analyse lie on properties of this type of polynomials and their measures along with their ratio asymptotic behaviour as well as the zero limit distribution. This talk is based on joint work with Walter Van Assche.