The d-dimensional bootstrap percolation models with axial neighbourhoods

Daniel Blanquicett

Stochastic Processes and their Applications, 2024, vol. 174, issue C

Abstract: Fix positive integers d,r and a1≤a2≤⋯≤ad. For large L, each site of {1,…,L}d⊂Zd can be at state 0 or 1 (infected), and its neighbourhood consists of the ak nearest neighbours in the ±ek-directions for each k∈{1,2,…,d}. The state will evolve in discrete time as follows: At time 0, vertices are independently 1 with some probability p. We infect any vertex v∈{1,…,L}d at state 0 already having r infected neighbours, and infected sites remain infected forever.

Keywords: Anisotropic bootstrap percolation; Cerf-Cirillo method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104383

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