We investigate the dynamics of a random walk in a random multiplicative medium. This results in a random, but correlated, multiplicative process for the spatial distribution of random walkers. We show how the details of these correlations determine the asymptotic properties of the walk, i.e., the central limit theorem does not apply to these multiplicative processes. We also study a periodic so...

We describe a family of random walks in random environments which have exponentially decaying correlations, nearest neighbor transition probabilities which are bounded away from 0, and yet are subdiffusive in any dimension d < o e .