PreprintarXiv licencearXiv
Some remarks on Talagrand's convolution conjecture
Abstract
We present self-contained martingale proofs of Talagrand's convolution conjecture in the Gaussian and Boolean settings with explicit dimension-free constants. The argument is based on the analysis of the stopped density martingale and a weighted Itô isometry estimate. The Gaussian case was settled by Eldan and Lee, and Lehec; the Boolean case was proved up to a loglog factor by Chen and recently settled by Lu, Guo and Fang.
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BibTeX
@misc{shaposhnikov2026some,
title = {{Some remarks on Talagrand's convolution conjecture}},
author = {Alexander Shaposhnikov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.11290},
eprint = {2609.11290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11290},
}
RIS
TY - UNPB
TI - Some remarks on Talagrand's convolution conjecture
AU - Alexander Shaposhnikov
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.11290
UR - https://arxiv.org/abs/2609.11290
AB - We present self-contained martingale proofs of Talagrand's convolution conjecture in the Gaussian and Boolean settings with explicit dimension-free constants. The argument is based on the analysis of the stopped density martingale and a weighted Itô isometry estimate. The Gaussian case was settled by Eldan and Lee, and Lehec; the Boolean case was proved up to a loglog factor by Chen and recently settled by Lu, Guo and Fang.
ER -