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Bizeul's conjecture: a dimension-free log-Sobolev inequality for log-concave measures with subgaussian linear marginals

Theorem 1.1: there is an absolute CC such that for every nn, every centered log-concave probability μ\mu on Rn\mathbb R^n with a density and linear subgaussian parameter aa, Entμ(f2)≤Ca2∫∣Df∣2dμ\mathrm{Ent}_\mu(f^2)\le Ca^2\int|Df|^2d\mu for all f∈Cc∞f\in C_c^\infty; this includes uniform measures on convex bodies and needs no smoothness or curvature. By Otto-Villani it gives the transport-entropy inequality W2(ν,μ)2≤Ca2H(ν∣μ)W_2(\nu,\mu)^2\le Ca^2H(\nu|\mu) with the same constant. Not given: a value of CC, or anything for non-log-concave measures.

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Bizeul's conjecture: a dimension-free log-Sobolev inequality for log-concave measures with subgaussian linear marginals · Bizeul's log-Sobolev conjecture

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VibeMathed record: Bizeul's conjecture: a dimension-free log-Sobolev inequality for log-concave measures with subgaussian linear marginals evidence for this event

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Bizeul's conjecture: a dimension-free log-Sobolev inequality for log-concave measures with subgaussian linear marginals evidence for this event

Theorem 1.1: there is an absolute CC such that for every nn, every centered log-concave probability μ\mu on Rn\mathbb R^n with a density and linear subgaussian parameter aa, Entμ(f2)≤Ca2∫∣Df∣2dμ\mathrm{Ent}_\mu(f^2)\le Ca^2\int|Df|^2d\mu for all f∈Cc∞f\in C_c^\infty; this includes uniform measures on convex bodies and needs no smoothness or curvature. By Otto-Villani it gives the transport-entropy inequality W2(ν,μ)2≤Ca2H(ν∣μ)W_2(\nu,\mu)^2\le Ca^2H(\nu|\mu) with the same constant. Not given: a value of CC, or anything for non-log-concave measures. parent of this event

Bizeul's conjecture: a dimension-free log-Sobolev inequality for log-concave measures with subgaussian linear marginals parent of this event

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