  We derive analytically the leading beyond-mean field contributions to the
zero-temperature equation of state and to the fermionic quasi-particle residue
and effective mass of a dilute Bose-Fermi mixture in two dimensions. In the
repulsive case, we perform quantum Monte Carlo simulations for two
representative bosonic concentrations and equal masses, extending a method for
correcting finite-size effects in fermionic gases to Bose-Fermi mixtures. We
find good agreement between analytic expressions and numerical results for weak
interactions, while significant discrepancies appear in the regime close to
mechanical instability, above which we provide evidence of phase separation of
the bosonic component.
