On the distribution of critical points of a polynomial

This paper proves that if points Z₁,Z₂,... are chosen independently and identically using some measure μ from the unit circle in the complex plane, with pₙ(z) = (z-Z₁)(z-Z₂)...(z-Zₙ), then the empirical distribution of the critical points of pₙ converges weakly to μ.