Noise sensitivity in bootstrap percolation
Abstract
Answering questions of Itai Benjamini, we show that the event of complete occupation in 2-neighbour bootstrap percolation on the d-dimensional box [n]d, for d≥ 2, at its critical initial density pc(n), is noise sensitive, while in k-neighbour bootstrap percolation on the d-regular random graph Gn,d, for 2≤ k≤ d-2, it is insensitive. Many open problems remain.
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