Chernoff's density is log-concave
  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. 
Fadoua Balabdaoui, Jon A. Wellner
math.ST stat.TH