Strong log-concavity of the Chernoff density

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

1. 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.

2. 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.