Normal approximation for iterated inner functions
Probability
2026-04-20 v1 Complex Variables
Functional Analysis
Abstract
A Berry--Ess\'{e}en theorem for linear combinations of iterates of an inner function is obtained. Our proof, which is based an elementary transfer argument and classical results in martingale theory, also leads to a simple proof of Nicolau and Soler i Gibert's central limit theorem for inner functions.
Cite
@article{arxiv.2604.16002,
title = {Normal approximation for iterated inner functions},
author = {Yukun Chen and Xiangdi Fu and Zhaofeng Lin and Yanqi Qiu},
journal= {arXiv preprint arXiv:2604.16002},
year = {2026}
}