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\geq 2, at its critical initial density p_c(n), is noise sensitive, while in k-neighbour bootstrap percolation on the d-regular random graph G_{n,d}, for 2\leq k\leq d-2, it is insensitive. Many open problems remain.

16 pages

References in corpus (3)

• Bootstrap percolation in three dimensions
• Quantitative relation between noise sensitivity and influences
• Quenched Voronoi percolation

Cited by in corpus (1)

• $\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications