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arXiv · 2609.11290

Some remarks on Talagrand's convolution conjecture

Alexander Shaposhnikov
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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 It\^o isometry estimate. The Gaussian case was settled by Eldan and Lee, and Lehec; the Boolean case was proved up to a $\log\log$ factor by Chen and recently settled by Lu, Guo and Fang.

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Alexander Shaposhnikov. 2026-09-10. Some remarks on Talagrand's convolution conjecture. https://arxiv.org/abs/2609.11290

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