  We study the dynamics of non-aligning, non-interacting self-propelled
particles confined to a box in two dimensions. In the strong confinement limit,
when the persistence length of the active particles is much larger than the
size of the box, particles stay on the boundary and align with the local
boundary normal. It is then possible to derive the steady-state density on the
boundary for arbitrary box shapes. In non-convex boxes, the non-uniqueness of
the boundary normal results in hysteretic dynamics and the density is
non-local, i.e. it depends on the global geometry of the box. These findings
establish a general connection between the geometry of a confining box and the
behavior of an ideal active gas it confines, thus providing a powerful tool to
understand and design such confinements.
