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Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals
Abstract
We study one-dimensional marginals of an isotropic, log-concave probability measure in ℝn. We show that the Kolmogorov distance between a typical marginal and the standard Gaussian distribution is at most C/n, for a universal constant C > 0. This bound is optimal in general, up to the value of the universal constant. It improves the Gaussian approximation bound of Bobkov, Chistyakov and Götze by a logarithmic factor in the log-concave setting.
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BibTeX
@misc{klartag2026revisiting,
title = {{Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals}},
author = {Boaz Klartag},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16740},
eprint = {2610.16740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16740},
}
RIS
TY - UNPB
TI - Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals
AU - Boaz Klartag
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16740
UR - https://arxiv.org/abs/2610.16740
AB - We study one-dimensional marginals of an isotropic, log-concave probability measure in ℝ^n. We show that the Kolmogorov distance between a typical marginal and the standard Gaussian distribution is at most C/n, for a universal constant C > 0. This bound is optimal in general, up to the value of the universal constant. It improves the Gaussian approximation bound of Bobkov, Chistyakov and Götze by a logarithmic factor in the log-concave setting.
ER -