关于Talagrand卷积猜想的一些注记
Some remarks on Talagrand's convolution conjecture
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中文总结 AI 辅助
本文通过鞅方法，利用停止密度鞅和加权伊藤等距估计，为高斯和布尔设定下的Talagrand卷积猜想提供了带显式无维常数的自包含证明。
中文摘要 AI 辅助
我们给出了Talagrand卷积猜想在高斯和布尔设定下的自包含鞅证明，并带有显式的无维常数。论证基于对停止密度鞅的分析以及一个加权伊藤等距估计。高斯情形由Eldan和Lee以及Lehec解决；布尔情形由Chen证明到$\log\log$因子，最近由Lu、Guo和Fang完全解决。
英文摘要
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 $\log\log$ factor by Chen and recently settled by Lu, Guo and Fang.
