We show that the density of Z = argmax{W (t) - t2}, 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.
Keywords: Brownian motion; Polya frequency function; Prekopa–Leindler theorem; Schoenberg’s theorem; airy function; correlation inequalities; hyperbolically monotone; log-concave; monotone function estimation; slope process; strongly log-concave.