Cellular automata related to self-organized criticality and their continuum limits

The concept of self-organized criticality (SOC) postulates a power-law distribution for the size of intermittent events in a large class of stochastic particle processes. We present a specific discrete model which satisfies many typical properties of this class, and which can be formally identified as the finite difference approximation of a stochastic porous medium equation with a singular-degenerate nonlinearity. We will pursue this aspect by proving that a sequence of suitably rescaled discrete processes of this kind indeed converges in law (in a weak topology) to the solution of the SPDE. This can be viewed as a contribution to the search for a universal limit equation of models displaying SOC.