Roots of random functions: A framework for local universality
Roots of random functions: A framework for local universality
We investigate the local distribution of roots of random functions of the form $F_n(z)=\sum_{i=1}^n\xi_i\phi_i(z)$, where $\xi_i$ are independent random variables and $\phi_i(z)$ are arbitrary analytic functions. Starting with the fundamental works of Kac and Littlewood-Offord in the 1940s, random functions of this type have been studied extensively in many fields …