A stochastic theory for temporal fluctuations in self-organized critical systems
Abstract
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 Itˆo
stochastic differential equation with an anti-persistent fractional Gaussian noise source.
An essential element of the theory is re-scaling to obtain a proper thermodynamic limit,
and it captures all temporal features of the toppling process obtained by numerical
simulation of the Bak-Tang-Wiesenfeld sandpile in this limit
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