On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2008,（1）
• 页码范围: 249-251
• 页数: 3页
• 语种: 英文

摘要

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. We assume that the variation of the number of active sites has three possibilities in each update: to increase by 1 with probability fl, to decrease by 1 with probability f2, or remain unchanged with probability 1-f1-f2. This mimics the dynamics in the system. Power-law distributions of the lifetime 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.