Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions

Viorel Barbu, Michael Röckner

If $X=X(t,\xi )$ is the solution to the stochastic porous media equation in $\mathcal{O}\subset {\mathbb{R}}^d$, $1\le d\le 3,$ modelling the self-organized criticaity and $X_c$ is the critic…