Asymptotics of the Number of Components of Random Polynomial Lemniscates

Subhajit Ghosh, Koushik Ramachandran, Atul Shekhar

Consider a sequence of random polynomials $P_n(z)={\prod }_{k=1}^n(z-X_k)$, where $\{X_k{\}}_k$ are i.i.d. random variables distributed uniformly on the unit disc $\mathbb{D}$. Le…