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Theory of Self-organized Criticality for Problems with Extremal Dynamics

A. Gabrielli·R. Cafiero·M. Marsili·L. Pietronero
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Abstract

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems.

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A. Gabrielli, R. Cafiero, M. Marsili, L. Pietronero. 1997-02-19. Theory of Self-organized Criticality for Problems with Extremal Dynamics. https://doi.org/10.1209/epl%2Fi1997-00273-1

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