Year: 2026
Type: preprint
Abstract: We study one-dimensional marginals of an isotropic, log-concave probability measure in $\mathbb{R}^n$. 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.
Source: arXiv (Cornell University)
Author: Klartag, Boaz
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G8365758310
OpenAlex ID: W7221804342