The sharp threshold for bootstrap percolation in all dimensions

@article{Balogh2010TheST,
  title={The sharp threshold for bootstrap percolation in all dimensions},
  author={J{\'o}zsef Balogh and B'ela Bollob'as and Hugo Duminil-Copin and Robert Morris},
  journal={arXiv: Probability},
  year={2010}
}
In r-neighbour bootstrap percolation on a graph G, a (typically random) set A of initially 'infected' vertices spreads by infecting (at each time step) vertices with at least r already-infected neighbours. This process may be viewed as a monotone version of the Glauber dynamics of the Ising model, and has been extensively studied on the d-dimensional grid $[n]^d$. The elements of the set A are usually chosen independently, with some density p, and the main question is to determine $p_c([n]^d,r… 

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