The Central Limit Theorem for inner functions II

Abstract

A sharp version of the Central Limit Theorem for linear combinations of iterates of an inner function is proved. The authors previously showed this result assuming a suboptimal condition on the coefficients of the linear combination. Here we explain a variation of the original argument which leads to the sharp result. We also review the steps of the proof as well as the main technical tool, which is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures.