PreprintCC BY 4.0HAL
Improved Bounds for the Entropic Central Limit Theorem in the Log-Concave Case
Abstract
Let μ be a log-concave isotropic probability measure on Rd , and let μn denote the law of the normalized sum of n independent random vectors with law µ. We prove that H(μn|γ)≤ C/n min{1+log(ed)2H(μ|γ) , d}. Compared to the previous best known bound, our estimate replaces the polynomial dependence on the dimension by a polylogarithmic one. The proof relies on a new combination of the De Bruijn identity with Eldan's stochastic localization process.
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BibTeX
@misc{maitre2026improved,
title = {{Improved Bounds for the Entropic Central Limit Theorem in the Log-Concave Case}},
author = {Tom Maitre},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31493},
eprint = {2610.31493},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05835605v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved Bounds for the Entropic Central Limit Theorem in the Log-Concave Case
AU - Tom Maitre
PY - 2026
DA - 2026/10/09
PB - HAL
DO - 10.48550/arxiv.2610.31493
UR - https://hal.science/hal-05835605v1
AB - Let μ be a log-concave isotropic probability measure on R^d , and let μ^n denote the law of the normalized sum of n independent random vectors with law µ. We prove that H(μ^n|γ)≤ C/n min{1+log(ed)^2H(μ|γ) , d}. Compared to the previous best known bound, our estimate replaces the polynomial dependence on the dimension by a polylogarithmic one. The proof relies on a new combination of the De Bruijn identity with Eldan's stochastic localization process.
ER -