  [Abridged] We test the reliability of a method to measure the mean halo mass
of Damped Ly-alpha absorbers (DLAs). The method is based on measuring the ratio
of the cross-correlation between DLAs and galaxies to the auto-correlation of
the galaxies themselves ($w_{\rm dg}/w_{\rm gg}$), which is (in linear theory)
the ratio of their bias factor. This is shown to be true irrespective of the
galaxy redshift distribution, provided that one uses the same galaxies for the
two correlation functions. The method is applicable to all redshifts. Here, we
focus on z=3 DLAs and we demonstrate that the method robustly constrains the
mean DLA halo mass using smoothed particle hydrodynamics (SPH) cosmological
simulations. If we use the bias formalism of Mo & White with the DLA and galaxy
mass distributions of these simulations, we predict a bias ratio of 0.771.
Direct measurement from the simulations of $w_{\rm dg}/w_{\rm gg}$ st yields a
ratio of 0.73+/-0.08, in excellent agreement with that prediction.
Equivalently, inverting the measured correlation ratio to infer a mean DLA halo
mass yields (log. averaging, in solar units) <log(M_DLA)> =11.13+/-013, in
excellent agreement with the true value in the simulations: 11.16. The cross-
correlation method thus appears to yield a robust estimate of the average host
halo mass even though the DLAs and the galaxies occupy a broad mass spectrum of
halos, and massive halos contain multiple galaxies with DLAs. We show that the
inferred mean DLA halo mass is independent of the galaxy sub-sample used, i.e.
the cross-correlation technique is also reliable. Our results imply that the
cross-correlation length between DLAs and LBGs is predicted to be, at most,
2.85 Mpc. Future observations will soon distinguish models in which DLAs are in
low mass halos from those in which DLAs are in massive halos.
