Selected research history · publication v8

Strong log-concavity of the Chernoff density

Follow the ideas, results and limitations over time. This is a selected history, not a complete literature survey or a measure of how close the problem is to being solved.

Current state & remaining question →

2 selected milestones · Source coverage checked 2026-10-14 · Historical annotation and mathematical review remain separate.

2014 publication
Related result
Log-concavity is proved and a stronger property proposed
Balabdaoui and Wellner publish ordinary log-concavity and conjecture uniform positive curvature.
Scope & review: This is a selected source-supported milestone, not an exhaustive history.
Statements & sources
- The earlier ordinary log-concavity theorem →
- Chernoff’s density is log-concave ↗Log-concavity theorem and Conjecture 3.1
Historical annotation review: pending. The date refers to the publication, with the precision supported by the source.
Jul 21, 2026 preprint
Related result
An analytic strong-curvature proof is submitted
Zhang and Zhou submit the selected preprint, crediting GPT-5.6 Sol and their own checking and exposition work.
Scope & review: This is the arXiv submission date. The selected manuscript’s title page says 24 August 2026; neither is asserted to be the discovery date.
Statements & sources
- Uniform positive curvature of the Chernoff density →
- Pointwise and tail curvature bounds →
- Chernoff’s Density Is Strongly Log-Concave ↗Theorem 1 and Section 5
Historical annotation review: pending. The date refers to the preprint, with the precision supported by the source.

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Log-concavity is proved and a stronger property proposed

An analytic strong-curvature proof is submitted