Self-organized criticality via stochastic partial differential equations
Probability
2018-06-18 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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.
Cite
@article{arxiv.0811.2093,
title = {Self-organized criticality via stochastic partial differential equations},
author = {Viorel Barbu and Philippe Blanchard and Giuseppe Da Prato and Michael Röckner},
journal= {arXiv preprint arXiv:0811.2093},
year = {2018}
}