Central limit theorems for the real zeros of Weyl polynomials

Yen Do, Van Vu

We establish the central limit theorem for the number of real roots of the Weyl polynomial $P_n(x)=x{i}_0+x{i}_{1}x+...+x{i}_n(n!{)}^{(-1/2)}{x}^n$, where $x{i}_i$ are iid Gaussian rando…