A Counterexample to the Gaussian Completely Monotone Conjecture
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910211448504320 |
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| author | Gu, Yuzhou Sellke, Mark |
| author_facet | Gu, Yuzhou Sellke, Mark |
| contents | We provide an explicit probability measure on $\mathbb{R}$ for which the fifth time derivative of the entropy along the heat flow is positive at some time. This disproves the Gaussian completely monotone (GCM) conjecture (Cheng-Geng '15) and therefore also the Gaussian optimality conjecture (McKean '66) and the entropy power conjecture (Toscani '15). Our proof also implies the existence of a log-concave probability measure on $\mathbb{R}$ for which the GCM conjecture fails at some order. The explicit counterexample was found by GPT-5.5 Pro. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Counterexample to the Gaussian Completely Monotone Conjecture Gu, Yuzhou Sellke, Mark Probability Information Theory We provide an explicit probability measure on $\mathbb{R}$ for which the fifth time derivative of the entropy along the heat flow is positive at some time. This disproves the Gaussian completely monotone (GCM) conjecture (Cheng-Geng '15) and therefore also the Gaussian optimality conjecture (McKean '66) and the entropy power conjecture (Toscani '15). Our proof also implies the existence of a log-concave probability measure on $\mathbb{R}$ for which the GCM conjecture fails at some order. The explicit counterexample was found by GPT-5.5 Pro. |
| title | A Counterexample to the Gaussian Completely Monotone Conjecture |
| topic | Probability Information Theory |
| url | https://arxiv.org/abs/2605.11656 |