The Berry--Esseen estimate in the Boolean central limit theorem

We estimate the Lévy distance to the symmetric Bernoulli distribution for normalized Boolean convolution powers of a probability measure with mean zero and variance one. If the absolute moment of order $r$ is finite, we obtain the upper bounds $o(n^{-(r-2)/6})$ for $2

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39743
Primary Topic
Random Matrices and Applications
Type
preprint
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preprint

The Berry--Esseen estimate in the Boolean central limit theorem

Noriyoshi Sakuma, Maejima Makoto
arXiv (Cornell University)
Random Matrices and Applications
preprint

The Berry--Esseen estimate in the Boolean central limit theorem

Noriyoshi Sakuma, Maejima Makoto
preprint en

Abstract

We estimate the Lévy distance to the symmetric Bernoulli distribution for normalized Boolean convolution powers of a probability measure with mean zero and variance one. If the absolute moment of order $r$ is finite, we obtain the upper bounds $o(n^{-(r-2)/6})$ for $2

arXiv (Cornell University)
Random Matrices and Applications
DOIOpen Access PDFOpenAlex
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The Berry--Esseen estimate in the Boolean central limit theorem — Noriyoshi Sakuma, Maejima Makoto · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS