On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment |
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Authors: | CAO Xiao-Feng DENG Zong-Wei YANG Chun-Bin |
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Institution: | Institute of Particle Physics, Huazhong Normal University, Wuhan 430079, China |
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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. We assume that the variation of the number of active sites has three possibilities in each update: to increase by 1 with probability f1, 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. |
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Keywords: | power-law distribution sell'organized criticality random walk |
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