Self-organized criticality via stochastic partial differential equations

Viorel Barbu, Philippe Blanchard, Giuseppe Da Prato, Michael Röckner

Published 2008-11-13Version 1

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.