Multifractal features of random walks on random fractals

We find that the fluctuations of the probability density P(r,t) of random walks on random fractals, for fixed distance r and time t, have a broad logarithmic distribution. The average moments Pq scale is a multifractal way, PqP(q), where (q)q, <1. The exponent characterizes the structural disorder in the fractal. In chemical l space, the distribution of P(l,t) is narrow and PqPq. © 1990 The American Physical Society.