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Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures

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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A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures

Sep 23, 2026·paper.pdf

We prove that every centered log-concave probability measure with a Lebesgue density on ℝ

^{n}

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.

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