Branching with local probability as a paradigm of self-organized criticality

A self-organized critical branching process based on a local interaction rule is presented. In accordance with the self-organized branching process model introduced by Zapperi, Lauritsen, and Stanley, its event-size distribution follows a power law with scaling exponent τ=3/2, but the new model does not require a global variable to self-organize to a critical point. The self-organized critical behavior of the model seems to be extremely robust. The model may be seen as a new paradigm for progressive mechanical failure (e.g., earthquakes or landslides) or other avalanching phenomena, and perhaps even for self-organized criticality in general.