Joseph Najnudel

On zeros of iterated derivatives of polynomials and randomizations

Limit theorems have been proven on the distributions of zeros of the k-th derivative of a polynomial of degree n, when k is small with respect to n or when the ratio k/n tends to a constant when n goes to infinity. In this talk, we discuss some of these results, and similar results proven when the derivative is replaced by some randomized versions related to the distribution of eigenvalues of unitarily invariant matrices.