  We consider a model for two types (bath and tracers) of 2D quantum particles
in a perpendicular magnetic field. Interactions are short range and
inter-species, and we assume that the bath particles are fermions, all lying in
the lowest Landau level of the magnetic field. Heuristic arguments then
indicate that, if the tracers are strongly coupled to the bath, they
effectively change their quantum statistics, from bosonic to fermionic or
vice-versa. We rigorously compute the energy of a natural trial state, indeed
exhibiting this phenomenon of statistics transmutation. The proof involves
estimates for the characteristic polynomial of the Ginibre ensemble of random
matrices.
