NUMBER OF DISTINCT SITES VISITED ON A PERCOLATION CLUSTER - CHARACTERIZATION OF FLUCTUATIONS

In continuation of previous work [L. K. Gallos, P. Argyrakis, and K. W . Kehr, Phys. Rev. E 52, 1520 (1995)], we present two additional analy ses in the search for possible multifractality of the distribution of (S-n), the mean number of distinct sites visited by a random walk in n steps on percolation clusters at their critical point. The first anal ysis utilizes the number of the different origins of the random walk a s the relevant size parameter. This analysis shows that the distributi on of(S-n) over different disorder environments is not a multifractal but rather exhibits constant gap scaling. In the second analysis, the moments of the distribution W((S-n)) are studied with respect to their n dependence. Here also constant gap scaling is observed.