  We study the higher-order correlation functions of covariant families of
observables associated with random Schr\"odinger operators on the lattice in
the strong disorder regime. We prove that if the distribution of the random
variables has a density analytic in a strip about the real axis, then these
correlation functions are analytic functions of the energy outside of the
planes corresponding to coincident energies. In particular, this implies the
analyticity of the density of states, and of the current-current correlation
function outside of the diagonal. Consequently, this proves that the
current-current correlation function has an analytic density outside of the
diagonal at strong disorder.
