Exactly soluble hierarchical clustering model: Inverse cascades, self-similarity, and scaling

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling,as an i ntermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as "self-organized critical," inc luding forest-fire, sandpile, and slider-Mock models. [S1063-651X(99)10511- 7].