Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 093-01. A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
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OpenAI@2026-10-07#rem:oai-p-093-01
Authors: OpenAI. Family 093.
Title: A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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