Self-organized random walks and stochastic sandpile

In a model of self-organized criticality unstable sites discharge to just one of their neighbours. For constant discharge ratio a and for a certain range of values of the input energy, avalanches are simple branchless Polya random walks, and their scaling properties can be derived exactly. If a fluctuates widely enough, avalanches become branched, due to multiple discharges, and behave like those of the stochastic sandpile. At the threshold for branched behaviour, peculiar scaling and anomalous diffusive transport are observed. (C) 2002 Elsevier Science B.V. All rights reserved.