Anti-concentration applied to roots of randomized derivatives of polynomials

André Galligo, Joseph Najnudel, Truong Vu

Let $(Z_k^{(n)}{)}_{1\le k\le n}$ be a random set of points and let ${\mu }_n$ be its \emph{empirical measure}: $${\mu }_n=\frac{1}{n}\sum _{k=1}^n{\delta }_{Z_k^{(n)}}.$$ Let $$P_n(z) := (z -…