  Scaling limits for the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW)
model for self-organized criticality are considered. It is shown that the
weakly driven Zhang model converges to a stochastic PDE with
singular-degenerate diffusion. In addition, the deterministic BTW model is
proved to converge to a singular-degenerate PDE. Alternatively, the proof of
convergence can be understood as a proof of convergence of a finite-difference
discretization for singular-degenerate stochastic PDE. This extends recent work
on finite difference approximation of (deterministic) quasilinear diffusion
equations to discontinuous diffusion coefficients and stochastic PDE.
