Scaling in self-organized criticality from interface depinning?

The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Alava M and Lauritsen K B 2001 Europhys. Lett. 53 569) of many sand-pile models to interface depinning is presented first, to provide an understanding of how to reach the SOC ensemble and the differences between this ensemble and the usual depinning scenario. In order to derive the SOC avalanche exponents from those of the depinning critical point, a geometric description of the quenched landscape, in which the `interface' measuring the integrated activity moves, is considered. It turns out that there are two main alternatives concerning the scaling properties of the SOC ensemble. These are outlined in one dimension in the light of scaling arguments and numerical simulations of a sandpile model which is in the quenched Edwards-Wilkinson universality class.