Central limits from generating functions

Mitchell Lee

Let $(Y_n{)}_n$ be a sequence of ${\mathbb{R}}^d$-valued random variables. Suppose that the generating function \[f(x, z) = \sum_{n = 0}^\infty φ_{Y_n}(x) z^n,\] where $\ddot{I}{†}_{Y_n}$ is t…