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arXiv · 0710.4010

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

Martin Rypdal·Kristoffer Rypdal
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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 Itô 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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Martin Rypdal, Kristoffer Rypdal. 2008-07-22. A stochastic theory for temporal fluctuations in self-organized critical systems. https://doi.org/10.1088/1367-2630%2F10%2F12%2F123010

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