  We model a quantum walk of identical particles that can change their exchange
statistics by hopping across a domain wall in a 1D lattice. Such a "statistical
boundary" is transparent to single particles and affects the dynamics only by
swapping multiple particles arriving together. We find that the two-particle
interference is dramatically altered by reflections of these bunched waves at
the interface, producing strong measurable asymmetries. Depending on the phases
on the two sides, a bunched wavepacket can get completely reflected or split
into a superposition of a reflected wave and an antibunched wave. This leads to
striking dynamics with two domain walls, where bunched waves can get trapped in
between or fragment into multiple correlated single-particle wavepackets. These
findings can be realized with density-dependent hopping in present-day atomic
setups and open up a new paradigm of intrinsically many-body phenomena at
statistical boundaries.
