The time of bootstrap percolation in two dimensions

We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on $$[n]^2$$[n]2 with initial set $$A\sim {\text {Bin}}([n]^2,p)$$A∼Bin([n]2,p). We determine T up to a constant factor with high probability for all p above the critical probability for percolation, and to within a $$1+o(1)$$1+o(1) factor for a large range of p.

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