Every centered log-concave probability measure with a Lebesgue density in R^n and linear a-subgaussian marginals satisfies a logarithmic Sobolev inequality with constant at most C a^2, uniformly in dimension.
Every centered log-concave probability measure with a Lebesgue density in R^n and linear a-subgaussian marginals satisfies a logarithmic Sobolev inequality with constant at most C a^2, uniformly in dimension.
Every centered log-concave probability measure with a Lebesgue density in R^n and linear a-subgaussian marginals satisfies a logarithmic Sobolev inequality with constant at most C a^2, uniformly in dimension.
If correct, resolves the dimension-free logarithmic Sobolev question for subgaussian log-concave measures.
Do subgaussian tails of every linear function force a dimension-free log-Sobolev inequality for log-concave measures?
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OpenAI reports a dimension-free log-Sobolev inequality from subgaussian marginals
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