Abstract. 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.

PACS numbers: 05.65.+b, 89.75.Da

Print publication: Issue 42 (22 October 2004)
Received 4 August 2004, in final form 20 September 2004
Published 6 October 2004