Resumen de Expected zeros of random orthogonal polynomials on the real line

Igor E. Pritsker

• We study the expected number of zeros for random linear combinations of orthogonal polynomials with respect to measures supported on the real line. The counting measures of zeros for these random polynomials converge weakly to the corresponding equilibrium measures from potential theory. We quantify this convergence and obtain asymptotic results on the expected number of zeros located in various sets of the plane. Random coefficients may be dependent and need not have identical distributions in our results.