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Theorem 1; reciprocal-Airy representation, exponential peeling, convolution identity, compactness and AI Usage.
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The Chernoff density factors as f(x) = C_f g(x)g(−x), where the normalized one-sided factor has reciprocal-Airy bilateral Laplace transform. The curvature is v(x)+v(−x).
Passage ID: chernoff-density:entry:factor:v1
Source item: factor
Source record: chernoff-density:source:paper:v1
The paper establishes v(x) > 0 and v(x) ≥ 4x for the normalized one-sided factor, hence κ(x) > 4|x| and inf κ > 0 for the Chernoff density.
Passage ID: chernoff-density:entry:theorem:v1
Source item: theorem
Source record: chernoff-density:source:paper: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
Proved
Airy factorization and curvature identity
The normalized one-sided factor and fixed Brownian/drift convention.
Source date Jul 21, 2026 · Observed Oct 14, 2026
Source assessment
Proved
Strong log-concavity proved in the selected preprint
Standard two-sided Brownian motion with unit quadratic drift; no explicit optimal uniform constant is asserted.
Source date Jul 21, 2026 · Observed Oct 14, 2026
Source assessment
Proved
Strong log-concavity proved in the selected preprint
Standard two-sided Brownian motion with unit quadratic drift; no explicit optimal uniform constant is asserted.
Source date Jul 21, 2026 · Observed Oct 14, 2026
Question
Strong log-concavity of the Chernoff density
Further reading
Inspect the normalized factor, transform domain and prior Airy identity.
Connection
The qualitative question asks for some uniform positive constant; the sharper 2014 conjecture specifies the origin curvature as the best constant.
Connection
The newer theorem strengthens ordinary log-concavity for the same distribution to a uniform strictly positive curvature bound.
Further reading
Read Theorem 1 and the compactness argument.
Recorded authorship
Xianyang Zhang · Quan Zhou
Xianyang Zhang, Quan Zhou
The authors attribute the proof to GPT-5.6 Sol, describe an initial algebraic failure and later corrected approaches, and report carefully checking the argument and revising the exposition.
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Chernoff’s Density Is Strongly Log-Concave
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