An asymptotic refinement of the Gauss-Lucas Theorem for random
polynomials with i.i.d. roots
An asymptotic refinement of the Gauss-Lucas Theorem for random
polynomials with i.i.d. roots
If $p:\mathbb{C} \to \mathbb{C}$ is a non-constant polynomial, the Gauss--Lucas theorem asserts that its critical points are contained in the convex hull of its roots. We consider the case when $p$ is a random polynomial of degree $n$ with roots chosen independently from a radially symmetric, compactly supported probably measure …