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 with initial set 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) factor for a large range of p.
Probability Theory and Related Fields
Balister, P., Bollobás, B., & Smith, P. (2016). The time of bootstrap percolation in two dimensions. Probability Theory and Related Fields, 166 (1-2), 321-364. https://doi.org/10.1007/s00440-015-0657-1