Chernoff's density is log-concave

TL;DR

This paper proves that Chernoff's density, arising from a specific stochastic process, is log-concave and discusses the conjecture that it is strongly log-concave or super-Gaussian, providing supporting evidence.

Contribution

It establishes the log-concavity of Chernoff's density and offers evidence for its stronger super-Gaussian property, a novel insight in the field.

Findings

Chernoff's density is proven to be log-concave.

Evidence supports the conjecture that it is strongly log-concave.

The paper discusses the potential super-Gaussian nature of Chernoff's density.

Abstract

We show that the density of $Z=\mathop {\operatorname {argmax}}\{W(t)-t^2\}$, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.