EQUILIBRIUM DISTRIBUTIONS FOR RANDOM WALKERS IN RANDOM-MEDIA

The authors study the Renyi entropies of the probability distribution of a random walker in a random medium of finite total volume. In one dimension of space it is shown that they tend, for large lattices, to constants independent of the lattice size. Thus, the distribution is not multifractal, in contrast to a recent claim. The authors conjecture that the same is true for any dimension if the random force is derived from a potential. In the more interesting general case (unconstrained forces), they cannot make a definite statement.