The origin of power-law distributions in self-organized criticality

TL;DR

This paper investigates the origins of power-law distributions in self-organized criticality by modeling avalanches as unbiased random walks, revealing that balance in interactions leads to these distributions.

Contribution

It introduces a stochastic process model of active site variation, linking unbiased random walks to power-law distributions in critical systems.

Findings

Power-law distributions occur when the random walk is unbiased.

The mean spatial size scales as a power law with lifetime.

Balance of interactions causes power-law behavior.

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.