Current correlations and quantum localization in a random or homogeneous magnetic field

We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic field) or correlation length of disorder. Performing a closely connected analysis of the quantum correction to the conductivity in one-loop order, we show that it is non-divergent, in contrast to recent claims in the literature.