Maximum Percolation Time in Two-Dimensional Bootstrap Percolation

@article{Benevides2015MaximumPT,
title={Maximum Percolation Time in Two-Dimensional Bootstrap Percolation},
author={Fabricio Siqueira Benevides and Michal Przykucki},
journal={SIAM J. Discrete Math.},
year={2015},
volume={29},
pages={224-251}
}

We consider a classical model known as bootstrap percolation on the n×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… CONTINUE READING