Published Bernoulli 20(1), 231–244; ordinary log-concavity and the stronger curvature conjecture.
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The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
The sharper original conjecture requires κ(x) ≥ κ(0) for every x. Its reported numerical value κ(0) ≈ 3.4052 is not established as a uniform lower bound by the selected 2026 theorem.
Passage ID: chernoff-density:entry:origin-minimum:v1
Source item: origin-minimum
Source record: chernoff-density:source:original:v1
Ordinary log-concavity is established, and uniform positive negative log-curvature is proposed as a stronger property of the same Chernoff density.
Passage ID: chernoff-density:entry:question:v1
Source item: question
Source record: chernoff-density:source:original:v1
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v8
Source assessment
Not assessed
Sharper origin-minimum conjecture in the original paper
The 2014 conjecture is recorded as a distinct quantitative target. The selected 2026 result does not establish its sharp constant; no current resolution is inferred from the older source.
Source date Feb 5, 2014 · Observed Oct 14, 2026
Source assessment
Proved
Published ordinary log-concavity theorem
The standard Chernoff density.
Source date Feb 5, 2014 · Observed Oct 14, 2026
Connection
The qualitative question asks for some uniform positive constant; the sharper 2014 conjecture specifies the origin curvature as the best constant.
Question
Strong log-concavity of the Chernoff density
Connection
The newer theorem strengthens ordinary log-concavity for the same distribution to a uniform strictly positive curvature bound.
History
Log-concavity is proved and a stronger property proposed
Further reading
Read the published theorem and the stronger conjecture.
Recorded authorship
Fadoua Balabdaoui · Jon A. Wellner
Fadoua Balabdaoui, Jon A. Wellner
No AI contribution is reported in this selected source.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
Chernoff’s density is log-concave
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