Random orthonormal polynomials: local universality and expected number of real roots

Yen Do, Oanh Nguyen, Van Vu

We consider random orthonormal polynomials $$F_n(x)=\sum _{i=0}^n{\xi }_i{p}_i(x),$$ where ${\xi }_0$, \dots, ${\xi }_n$ are independent random variables with zero mean, unit variance…