  The zero-temperature Hall response within tight-binding models of correlated
electrons is studied. Using the linear response theory and a linearization in
the magnetic field B, a general relation for the reactive (zero frequency) Hall
constant in the fast (transport) limit is derived, involving only matrix
elements between the lowest excited states at B=0; for noninteracting fermions,
the Boltzmann expression is reproduced. For a Fermi liquid with a well defined
Fermi surface and linear gapless excitations an analogous expression is found
more generally. In the specific case of quasi-one-dimensional correlated
systems a relation of $R^0_H$ to the charge stiffness D is recovered. Similar
analysis is performed and discussed for D and the compressibility.
