Metastability Thresholds for Anisotropic Bootstrap Percolation in Three Dimensions

In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally...

Metastability thresholds for anisotropic bootstrap percolation in three dimensions

In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally...

Growth Rates and Explosions in Sandpiles

We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Zd . Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h ? 2d ? 2, the diameter of the set of sites that topple has order n1/d. This...