Noise sensitivity in bootstrap percolation
Probability
2015-09-29 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1509.08454,
title = {Noise sensitivity in bootstrap percolation},
author = {Zsolt Bartha and Gábor Pete},
journal= {arXiv preprint arXiv:1509.08454},
year = {2015}
}
Comments
16 pages