Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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.
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MANUSCRIPT 01
A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures
We prove that every centered log-concave probability measure with a Lebesgue density on ℝ^(n) and linear subgaussian parameter a satisfies \mathop{Ent}\nolimits _\mu(f^2)≤ Ca^2\int|Df|^2d\mu for compactly supported smooth f, with one universal constant C. This resolves positively the dimension-free logarithmic Sobolev…
Full source abstract
We prove that every centered log-concave probability measure with a Lebesgue density on ℝ^(n) and linear subgaussian parameter a satisfies \mathop{Ent}\nolimits _\mu(f^2)≤ Ca^2\int|Df|^2d\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.
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