A stochastic theory for temporal fluctuations in self-organized critical systems
Statistical Finance
2009-11-13 v2 Adaptation and Self-Organizing Systems
Cellular Automata and Lattice Gases
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 It\^{o} 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.
Cite
@article{arxiv.0710.4010,
title = {A stochastic theory for temporal fluctuations in self-organized critical systems},
author = {Martin Rypdal and Kristoffer Rypdal},
journal= {arXiv preprint arXiv:0710.4010},
year = {2009}
}
Comments
9 pages, 4 figures