Range of multifractality for random walks on random fractals

We study the range of multifractality for the probability density P(r,t) of random walks on linear random fractals, for a given distance r and time t. Analytical study of the moments Pq(r,t) shows that multifractality exists only when 1<qrwd/t and qr/t<1, with dw=2df, where df is the fractal dimension of the linear fractal. The results can be extended to more general random fractals and are consistent with recent numerical data for the form of P(r,t).