THEORY OF EXTREMAL DYNAMICS WITH QUENCHED DISORDER - SELF-ORGANIZATION, AVALANCHE DYNAMICS AND CRITICAL EXPONENTS

In this paper we discuss a general theoretical scheme, that we have re cently proposed, for a class of phenomena characterized by extremal dy namics with quenched disorder. The approach is based on a transformati on of the quenched dynamics into a stochastic dynamics with cognitive memory. This transformation, together with other concepts, permits a m athematical characterization of the self-organized nature of the avala nche type dynamics. By combining the mapping with real space methods, like the fixed scale transformation (FST), it is also possible to comp ute the relevant critical exponents directly from the microscopic mode l. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems with quench ed disorder.