Central limit theorems and the geometry of polynomials

Marcus Michelen, Julian Sahasrabudhe

Let $X\in \{0,\dots ,n\}$ be a random variable, with mean $\mu$ and standard deviation $\sigma$ and let \[f_X(z) = \sum_{k} \mathbb{P}(X = k) z^k, \] be its probability generating funct…