  We propose an analytical method to determine the shape of density profiles in
the asymptotic long time limit for a broad class of coupled continuous time
random walks which operate in the ballistic regime. In particular, we show that
different scenarios of performing a random walk step, via making an
instantaneous jump penalized by a proper waiting time or via moving with a
constant speed, dramatically effect the corresponding propagators, despite the
fact that the end points of the steps are identical. Furthermore, if the speed
during each step of the random walk is itself a random variable, its
distribution gets clearly reflected in the asymptotic density of random
walkers. These features are in contrast with more standard non-ballistic random
walks.
