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arXiv · 2607.18619

Chernoff's Density Is Strongly Log-Concave

Xianyang Zhang·Quan Zhou
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Abstract

Let $f$ be the density of the Chernoff random variable $\mathrm{argmax}_{t\in\mathbb{R}}\{W(t)-t^2\}$, where $W$ is a two-sided Brownian motion. This note proves the conjecture of Balabdaoui and Wellner (2014) that $f$ is strongly log-concave. The proof was generated in its entirety by GPT-5.6 Sol.

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Xianyang Zhang, Quan Zhou. 2026-07-21. Chernoff's Density Is Strongly Log-Concave. https://arxiv.org/abs/2607.18619

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