The location of the unique supremum of
a stationary process on an interval does not need to be uniformly
distributed over that interval. We describe all possible distributions
of the supremum
location for a broad class of such stationary processes. We show that,
in the strongly mixing case, this distribution does tend to the
uniform in a certain sense as the length of the interval increases to
infinity. ARO
grant W911NF-07-1-0078, NSF grant DMS-1005903 and NSA grant
H98230-11-1-0154