PreprintarXiv licencearXiv
The Berry-Esseen Constant Conjecture is Eventually True
Abstract
We prove that the Esseen's constant $0.4097...$ is valid in the iid Berry--Esseen inequality as long as the sample sizes n≥ N. The threshold N is universal over all real summand distributions with positive variance and a finite third absolute moment. In particular, one may take $N=2\left\lceil\exp(10^{17})\right\rceil. $
Related
- The multivariate Berry-Esseen theorem with an absolute constant
- Berry--Esseen theorems, LLT, Edgeworth expansions, and large deviations for Locally Stationary Markov Chains
- The Berry--Esseen estimate in the Boolean central limit theorem
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- Berry--Esseen bounds for stochastic approximation with Markovian noise
BibTeX
@misc{he2026berryesseen,
title = {{The Berry-Esseen Constant Conjecture is Eventually True}},
author = {Hengzhi He and Guang Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06358},
eprint = {2609.06358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06358},
}
RIS
TY - UNPB
TI - The Berry-Esseen Constant Conjecture is Eventually True
AU - Hengzhi He
AU - Guang Cheng
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.06358
UR - https://arxiv.org/abs/2609.06358
AB - We prove that the Esseen's constant $0.4097...$ is valid in the iid Berry--Esseen inequality as long as the sample sizes n≥ N. The threshold N is universal over all real summand distributions with positive variance and a finite third absolute moment. In particular, one may take $N=2\left\lceil\exp(10^{17})\right\rceil. $
ER -