Random Multiplicative Processes and Transport in Structures with Correlated Spatial Disorder

We show that strong spatial correlations in a random resistor network can dramatically alter its transport properties. We calculate the average logarithmic resistance of a topologically one-dimensional model characterized by a random multiplicative process. We find a transport exponent that depends explicitly on the form of the spatial correlations; we also find that this problem is related to diffusion in the presence of correlated random fields.