Deterministic bootstrap percolation in high dimensional grids

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.

This paper has been withdrawn by the authors since Theorem 3.1 has been proved in an earlier paper

References in corpus (1)

• Bootstrap percolation on the random graph $G_{n,p}$

Cited by in corpus (1)

• Bootstrap percolation in Ore-type graphs