  We employed the method of virial expansion in order to compute the retarded
density correlation function (generalized diffusion propagator) in the critical
random matrix ensemble in the limit of strong multifractality. We found that
the long-range nature of the Hamiltonian is a common root of both
multifractality and Levy flights which show up in the power-law intermediate-
and long-distance behavior, respectively, of the density correlation function.
We review certain models of classical random walks on fractals and show the
similarity of the density correlation function in them to that for the quantum
problem described by the random critical long-range Hamiltonians.
