Selforganized criticality via stochastic partial differential equations
Abstract
Models of selforganized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld and Zhangmodels), are analyzed. Existence and uniqueness of nonnegative strong solutions are proved. Previously numerically predicted transition to the critical state in 1D is confirmed by a rigorous proof that this indeed happens in finite time with high probability.
 Publication:

arXiv eprints
 Pub Date:
 November 2008
 arXiv:
 arXiv:0811.2093
 Bibcode:
 2008arXiv0811.2093B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 Theta Series in Advanced Mathematics, "Potential Theory and Stochastic Analysis" in Albac. Aurel Cornea Memorial Volume, 2009, pp. 1119