The time of bootstrap percolation in two dimensions

Abstract

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

39 pages, 6 figures

References in corpus (2)

• Bootstrap percolation in three dimensions
• Monotone cellular automata in a random environment

Cited by in corpus (2)

• Two Phase Transitions in Two-way Bootstrap Percolation
• The time of bootstrap percolation with dense initial sets for all thresholds