OpenAI · 093-01 · 2026-09-23 · Convex and metric geometry
A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
preprints/A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026
Family 093. Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
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.
We prove that every centered log-concave probability measure with a Lebesgue density on ℝn and linear subgaussian parameter a satisfies for compactly supported smooth f, with one universal constant C. This resolves positively the dimension-free logarithmic Sobolev conjecture for subgaussian log-concave measures.
Preprint source and Lean scope
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