Levy flights and multifractality in quantum critical diffusion and in   classical random walks on fractals
  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. 
V. E. Kravtsov, O. M. Yevtushenko, P. Snajberk, and E. Cuevas
cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP