Title: Local Density Approximation for Almost-Bosonic Anyons,
Abstract: We discuss the average-field approximation for a trapped gas of
non-interacting anyons in the quasi-bosonic regime. In the homogeneous case,
i.e., for a confinement to a bounded region, we prove that the energy in the
regime of large statistics parameter, i.e., for "less-bosonic" anyons, is
independent of boundary conditions and of the shape of the domain. When a
non-trivial trapping potential is present, we derive a local density
approximation in terms of a Thomas-Fermi-like model.