  Polygonal billiards are an example of pseudo-chaotic dynamics, a combination
of integrable evolution and sudden jumps due to conical singular points that
arise from the corners of the polygons. Even when pseudo-chaos is characterised
by an algebraic separation of nearby trajectories, it is believed to be linked
to the wild dependence that particle transport has on the fine details of
billiards' shape. Here we address this relation by studying in detail the
statistics of the particle's displacement in a family of polygonal open
channels with parallel walls. We show that transport is characterised by strong
anomalous diffusion, with a mean square displacement that scales in time faster
than linear, and with a probability density of the displacement exhibiting
exponential tails and ballistic fronts. In channels of finite length the
distribution of first-passage time to escape the channel is characterised by
fat tails, with a mean first-passage time that diverges when the aperture angle
is rational. These findings have non trivial consequences for a variety of
experiments.
