Emergence of fractional statistics for tracer particles in a Laughlin liquid

We consider a thought experiment where two distinct species of 2D particles in a perpendicular magnetic field interact via repulsive potentials. If the magnetic field and the interactions are strong enough, one type of particles forms a Laughlin state and the other ones couple to Laughlin quasi-holes. We show that in this situation, the motion of the second type of particles is described by an effective Hamiltonian, corresponding to the magnetic gauge picture for non-interacting anyons. The argument is in accord with, but distinct from, the Berry phase calculation of Arovas-Schrieffer-Wilczek. It suggests possibilities to observe the influence of effective anyon statistics in fractional quantum Hall systems.