13 research outputs found
Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections
In this note we analyze an anisotropic, two-dimensional bootstrap percolation
model introduced by Gravner and Griffeath. We present upper and lower bounds on
the finite-size effects. We discuss the similarities with the semi-oriented
model introduced by Duarte.Comment: Key words: Bootstrap percolation, anisotropy, finite-size effect
Metastability threshold 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
threshold 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 determined by the "easiest growth
direction" in the model. In contrast to the anisotropic bootstrap percolation
in two dimensions, in three dimensions the order of the metatstability
threshold for anisotropic bootstrap percolation can be equal to that of
isotropic bootstrap percolation.Comment: 19 page