Deterministic bootstrap percolation in high dimensional grids
Combinatorics
2013-09-05 v2
Abstract
In this paper, we study the k-neighbor bootstrap percolation process on the d-dimensional grid [n]^d, and show that the minimum number of initial vertices that percolate is (1-d/k)n^d + O(n^{d-1})$ when d<=k<=2d. This confirms a conjecture of Pete.
Keywords
Cite
@article{arxiv.1308.6791,
title = {Deterministic bootstrap percolation in high dimensional grids},
author = {Hao Huang and Choongbum Lee},
journal= {arXiv preprint arXiv:1308.6791},
year = {2013}
}
Comments
This paper has been withdrawn by the authors since Theorem 3.1 has been proved in an earlier paper