Moderate Deviations for Functionals over infinitely many Rademacher random variables

TL;DR

This paper develops moderate deviation results for normal approximation of functionals involving infinitely many Rademacher variables, using Malliavin--Stein techniques and applications to random graphs and 2-runs.

Contribution

It introduces new bounds for the Kolmogorov distance and extends moderate deviation principles to complex Rademacher functionals.

Findings

Bound for Kolmogorov distance between Rademacher functional and Gaussian

Moderate deviation principles established for subgraph counts

Analysis of infinite weighted 2-runs

Abstract

In this paper, moderate deviations for normal approximation of functionals over infinitely many Rademacher random variables are derived. They are based on a bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, continued by an intensive study of the behavior of operators from the Malliavin--Stein method along with the moment generating function of the mentioned functional. As applications, subgraph counting in the Erd\H{o}s--R\'enyi random graph and infinite weighted 2-runs are studied.