{"id":"openai-math/A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures","pdf":"https://github.com/openai/math/blob/main/preprints/A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-dimension-free-logarithmic-Sobolev-inequality-for-subgaussian-log-concave-measures-September-23-2026","tags":["probability","functional-inequalities","log-concave","analysis"],"score":0,"title":"A dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures","domain":"Convex and metric geometry","family":"093","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures"}