Markov Chain Hidden behind Power Law Mechanism of Self-organized Criticality
De Tao Mao, Yisheng Zhong

TL;DR
This paper introduces a four-state Markov model to analytically derive the power law distribution in Self-Organized Criticality systems, offering a new theoretical perspective on the universality of power laws.
Contribution
It presents a novel Markov model and a mathematical proof that explain the power law distribution in SOC, expanding understanding beyond simulation-based approaches.
Findings
Derived a mathematical proof of power law distribution in SOC
Showed the universality of power laws in a broader class of dynamical systems
Provided a new analytical framework for SOC analysis
Abstract
To describe and analyze the dynamics of Self-Organized Criticality (SOC) systems, a four-state continuous-time Markov model is proposed in this paper. Different to computer simulation or numeric experimental approaches commonly employed for explaining the power law in SOC, in this paper, based on this Markov model, using E.T.Jayness' Maximum Entropy method, we have derived a mathematical proof on the power law distribution for the size of these events. Both this Makov model and the mathematical proof on power law present a new angle on the universality of power law distributions, they also show that the scale free property exists not necessary only in SOC system, but in a class of dynamical systems which can be modelled by the proposed Markov model.
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Taxonomy
TopicsTheoretical and Computational Physics · Complex Network Analysis Techniques · Complex Systems and Time Series Analysis
