A stochastic theory for temporal fluctuations in self-organized critical systems

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the Ito stochastic differential equation with an anti-persistent fractional Gaussian noise source and a deterministic drift term. An essential element of the theory is rescaling to obtain a proper thermodynamic limit. When subjected to the most relevant statistical tests, the signal generated by the stochastic equation is indistinguishable from the temporal features of the toppling process obtained by numerical simulation of the Bak-Tang-Wiesenfeld sandpile.