Proves a dimension-free logarithmic Sobolev inequality for centered log-concave densities with uniformly subgaussian linear marginals, with constant bounded by a universal multiple of the squared linear subgaussian parameter.
Manuscript
A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
September 23, 2026 · source · cite as \cite{OAI:A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026}
We prove that every centered log-concave probability measure with a Lebesgue density on ℝn and linear subgaussian parameter a satisfies \mathop{\mathrm{Ent}}\nolimits _\mu(f^2)\le Ca^2\int|Df|^2\,d\mu for compactly supported smooth f, with one universal constant C. This resolves positively the dimension-free logarithmic Sobolev conjecture for subgaussian log-concave measures.
Result 093 · Convex and metric geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md