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      Maximum percolation time in two-dimensional bootstrap percolation

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          Abstract

          We consider a classic model known as bootstrap percolation on the \(n \times n\) square grid. To each vertex of the grid we assign an initial state, infected or healthy, and then in consecutive rounds we infect every healthy vertex that has at least \(2\) already infected neighbours. We say that percolation occurs if the whole grid is eventually infected. In this paper, contributing to a recent series of extremal results in this field, we prove that the maximum time a bootstrap percolation process can take to eventually infect the entire vertex set of the grid is \(13n^2/18+O(n)\).

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          Most cited references 10

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          Bootstrap percolation on a Bethe lattice

           J Chalupa,  P Leath,  G R Reich (1979)
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            Metastability effects in bootstrap percolation

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              Sharp metastability threshold for two-dimensional bootstrap percolation

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                Author and article information

                Journal
                16 October 2013
                2014-11-05
                Article
                1310.4457

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                28 pages
                math.CO

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