Strong Log-Concavity of Chernoff's Density
Is the density of Chernoff's distribution - the law of for two-sided Brownian motion - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Probability & statistics
- Posed by
- Fadoua Balabdaoui & Jon A. Wellner
- Year posed
- 2014
- Years open
- 12y
- Solved
- 2026-07-21
- Model
- GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Xianyang Zhang, Quan Zhou
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The proof was generated in its entirety by GPT-5.6 Sol; the authors checked it and prepared the manuscript.
Verification
Author-checked public arXiv preprint. Not yet peer-reviewed.
Source
arXiv:2607.18619 - Chernoff's density is strongly log-concave