The Common Limit of the Linear Statistics of Zeros of Random Polynomials and Their Derivatives

I-Shing Hu, Chih-Chung Chang

Let $p_n(x)$ be a random polynomial of degree $n$ and $\{Z_j^{(n)}{\}}_{j=1}^n$ and $\{X_j^{n,k}{\}}_{j=1}^{n-k},k<n$, be the zeros of $p_n$ and $p_n^{(k)}$, the $k$th derivative o…