THEORY OF SELF-ORGANIZED CRITICALITY FOR PROBLEMS WITH EXTREMAL DYNAMICS

We introduce a general theoretical scheme for a class of phenomena cha racterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochast ic one with cognitive memory and on other concepts which permit a math ematical characterization of the self-organized nature of the avalanch e type dynamics. In addition it is possible to compute the relevant cr itical exponents directly from the microscopic model. A specific appli cation to invasion percolation is presented but the approach can be ea sily extended to various other problems.