Abstract. We generalize Einstein’s master equation for random walk processes by considering that the probability for a particle at position r to make a jump of length j lattice sites, Pj(r) is a functional of the particle distribution function f(r, t). By multiscale expansion, we obtain a generalized advection-diffusion equation. We show that the power law Pj(r) ∝ f(r) α−1 (with α > 1) follows ...