Talagrand’s convolution conjecture

Lineage and corrections

Corrects Talagrand’s convolution conjecture →

Supersedes Talagrand’s convolution conjecture →

O'Donnell's open-problem list, where the conjecture and its $1000 prize are recorded evidence for this event

Talagrand’s convolution conjecture evidence for this event

Xiang and Zhang, Layerwise terminal discrepancy in Chen's reverse-heat coupling (June 2026) evidence for this event

The claim is the exact conjectured decay: $\psi_{\mu_a}(u) \le C_a/\sqrt{\log u}$ for every $u > 1$ and every $n$, with $C_a$ dimension-free - concretely $\lesssim \kappa_a^2(\log\frac{\kappa_a}{\kappa_a-1})^{1/2}$ where $\kappa_a = (1+a)/(1-a)$. What is new is one step in a three-paper chain rather than a proof from scratch, and the paper is explicit about it. Chen's reverse-heat and Boolean-bridge framework and Xiang-Zhang's localized terminal-discrepancy method are taken as given; the addition is a power coupling that splits each reverse edge ratio into two geometric powers, producing a switched exponential weight that restores the exact reverse jump rate of the perturbed coordinate. Because the frozen exponent then has a fixed numerator, no growing stopping buffer is needed and the $\log\log u$ factor disappears. That last $\log\log$ is what stood between the previous work and Talagrand's statement. parent of this event

Chen, Talagrand's convolution conjecture up to loglog via perturbed reverse heat (Nov 2025) evidence for this event

This event attributed to Odin Automatic AI Research Agent

This event attributed to Junwei Lu

This event attributed to Shengtao Guo

VibeMathed record: Talagrand’s convolution conjecture evidence for this event

Talagrand’s convolution conjecture parent of this event

This event attributed to Ethan X. Fang