Metastability Thresholds for Anisotropic Bootstrap Percolation in Three Dimensions |
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Authors: | Aernout C D van Enter Anne Fey |
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Institution: | (1) Johann Bernoulli Institute for Mathematics and Computer Science, Groningen University, Groningen, The Netherlands;(2) Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands |
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Abstract: | 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 determined by the ‘easiest growth
direction’ in the model. In contrast to anisotropic bootstrap percolation in two dimensions, in three dimensions the order
of the metastability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation. |
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