Weak Non-self-averaging Behavior For Diffusion In A Trapping Environment

The statistics of equally weighted random paths (ideal polymer) is studied in two- and three dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of step walks, N, follows a logarithmic-normal distribution with a:variance growing asymptotically faster than the mean, which leads to a weak non-self-averaging behavior. Critical exponents associated with the scaling of the two-point correlation function do not obey standard scaling laws.