A Berry Esseen type limit theorem for Boolean convolution

TL;DR

This paper provides estimates on the rate of convergence in the Boolean central limit theorem using the Lévy distance, including sharp bounds for measures with bounded support.

Contribution

It introduces new bounds on the convergence rate in the Boolean CLT, especially for measures with bounded support, enhancing understanding of Boolean convolution limits.

Findings

Derived estimates on convergence rates in Boolean CLT

Provided sharp bounds for measures with bounded support

Quantified convergence in Lévy distance

Abstract

We give estimates on the rate of convergence in the Boolean central limit theorem for the L\'evy distance. In the case of measures with bounded support we obtain a sharp estimate by giving a qualitative description of this convergence.