  We use time-resolved measurement and modeling to study the spin-torque
induced motion of a domain wall in perpendicular anisotropy magnets. In disc of
diameters between 70 and 100 nm, the wall drifts across the disc with
pronounced back-and-forth oscillations that arise because the wall moves in the
Walker regime. Several switching paths occur stochastically and lead to
distinct switching durations. The wall can cross the disc center either in a
ballistic manner or with variably marked oscillations before and after the
crossing. The crossing of the center can even occur multiple times if a
vertical Bloch line nucleates within the wall. The wall motion is analyzed
using a collective coordinate model parametrized by the wall position $q$ and
the tilt $\phi$ of its in-plane magnetization projection. The dynamics results
from the stretch field, which describes the affinity of the wall to reduce its
length and the wall stiffness field describing the wall tendency to reduce
dipolar energy by rotating its tilt. The wall oscillations result from the
continuous exchange of energy between to the two degrees of freedom $q$ and
$\phi$. The stochasticity of the wall dynamics can be understood from the
concept of the retention pond: a region in the $q-\phi$ space in which walls
are transiently bound to the disc center. Walls having trajectories close to
the pond must circumvent it and therefore have longer propagation times. The
retention pond disappears for a disc diameter of typically 40 nm: the wall then
moves in a ballistic manner irrespective of the dynamics of its tilt. The
propagation time is then robust against fluctuations hence reproducible.
