Pairing between zeros and critical points of random polynomials

Boris Hanin

Consider a polynomial p_N(z) in one complex variable. The Gauss-Lucas Theorem says that the critical points of p_N lie inside the convex hull of its zeros. But are critical points actually distributed inside the convex hull if p_N is chosen at random?

http://scgp.stonybrook.edu/video_portal/video.php?id=1579

Simons- Program: Large N limit problems in Kahler Geometry