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The d-dimensional bootstrap percolation models with axial neighbourhoods

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  • Blanquicett, Daniel

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.

Suggested Citation

  • Blanquicett, Daniel, 2024. "The d-dimensional bootstrap percolation models with axial neighbourhoods," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000899
    DOI: 10.1016/j.spa.2024.104383
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    References listed on IDEAS

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    1. Cerf, R. & Manzo, F., 2002. "The threshold regime of finite volume bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 69-82, September.
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