  We calculate the phase diagram for dilute mixtures of bosons and fermions at
zero temperature. The linear stability conditions are derived and related to
the effective boson-induced interaction between the fermions. We show that in
equilibrium there are three possibilities: a) a single uniform phase, b) a
purely fermionic phase coexisting with a purely bosonic one and c) a purely
fermionic phase coexisting with a mixed phase.
