  We generalize the predictions for attractions between over-all neutral
surfaces induced by charge fluctuations/correlations to non-uniform systems
that include dielectric discontinuities, as is the case for mixed charged lipid
membranes in an aqueous solution. We show that the induced interactions depend
in a non-trivial way on the dielectric constants of membrane and water and show
different scaling with distance depending on these properties. The generality
of the calculations also allows us to predict under which dielectric conditions
the interaction will change sign and become repulsive.
