Self-organized criticality attributed to a central limit-like convergence effect

Wayne S. Kendal

Physica A: Statistical Mechanics and its Applications, 2015, vol. 421, issue C, 141-150

Abstract: Self-organized criticality is a hypothesis used to explain the origin of 1/f noise and other scaling behaviors. Despite being proposed nearly 30 years ago, no consensus exists as to its exact definition or mathematical mechanism(s). Recently, a model for 1/f noise was proposed based on a family of statistical distributions known as the Tweedie exponential dispersion models. These distributions are characterized by an inherent scale invariance that manifests as a variance to mean power law, called fluctuation scaling; they also serve as foci of convergence in a limit theorem on independent and identically distributed distributions. Fluctuation scaling can be modeled by self-similar stochastic processes that relate the variance to mean power law to 1/f noise through their correlation structure. A hypothesis is proposed whereby the effects of self-organized criticality are mathematically modeled by the Tweedie distributions and their convergence behavior as applied to self-similar stochastic processes. Sandpile model fluctuations are shown to manifest 1/f noise, fluctuation scaling, and to conform to the Tweedie compound Poisson distribution. The Tweedie models and their convergence theorem allow for a mechanistic explanation of 1/f noise and fluctuation scaling in phenomena conventionally attributed to self-organized criticality, thus providing a paradigm shift in our understanding of these phenomena.

Keywords: Sandpile model; Tweedie exponential dispersion models; 1/f noise; Fluctuation scaling; Multifractality; Taylor’s power law (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:421:y:2015:i:c:p:141-150

DOI: 10.1016/j.physa.2014.11.035

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