C. B. Yang
Published 2004-03-11, updated 2004-10-02Version 2
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.
Comments: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in J. Phys. A
Journal: J. Phys. A 37, L523 (2004)
1/f noise from correlations between avalanches in self-organized criticality
Nonstationary but quasisteady states in Self-organized Criticality
Emergence and complexity in theoretical models of self-organized criticality
