Self-organized criticality via stochastic partial differential equations

Details Self-organized criticality via stochastic partial differential equations Self-organized criticality via stochastic partial differential equations

2008-11-13

arxiv.org/abs/0811.2093v1

Mathematics

Probability

Scientific paper

Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of nonnegative strong solutions are proved. Previously numerically predicted transition to the critical state in 1-D is confirmed by a rigorous proof that this indeed happens in finite time with high probability.

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