Subcritical \mathcal{U}-bootstrap percolation models have non-trivial phase transitions

Recently Bollob]]>á. This is new except for a certain `degenerate' subclass of symmetric models that can be coupled from below with oriented site percolation. Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices, and they allow one to ask many...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2016-10, Vol.368 (10), p.7385-7411
Main Authors: Balister, Paul, Bollobás, Béla, Przykucki, Michał, Smith, Paul
Format: Article
Language:English
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Summary:Recently Bollob]]>á. This is new except for a certain `degenerate' subclass of symmetric models that can be coupled from below with oriented site percolation. Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices, and they allow one to ask many questions of subcritical bootstrap percolation models that are typically asked of site or bond percolation.]]>
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6586