We review various formulations of conductivity for one-particle Hamiltonians
and relate them to the current-current correlation measure. We prove that the
current-current correlation measure for random Schr\"odinger operators has a
density at coincident energies provided the energy lies in a localization
regime. The density vanishes at such energies and an upper bound on the rate of
vanishing is computed. We also relate the current-current correlation measure
to the localization length
