SELF-ORGANIZED BRANCHING-PROCESSES - MEAN-FIELD THEORY FOR AVALANCHES

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point ou t that the nature of the self-organization is not addressed properly b y the previously proposed mean-field theories. We introduce a new mean -field model that explicitly takes the boundary conditions into accoun t; in this way, the local dynamical rules are coupled to a global equa tion that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche dist ributions.