Natural boundary and zero distribution of random polynomials in smooth domains

Igor Pritsker, Koushik Ramachandran

We consider the zero distribution of random polynomials of the form $P_n(z)={\sum }_{k=0}^n{a}_k{B}_k(z)$, where $\{a_k{\}}_{k=0}^{\infty }$ are non-trivial i.i.d. complex random variabl…