We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular (artificial) magnetic field. Interactions are short range and only 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 is based on (seemingly ?) new estimates for the characteristic polynomial of the Ginibre ensemble of random matrices.
Joint work with Douglas Lundholm and Gaultier Lambert