pith. sign in

arxiv: 1308.6791 · v2 · pith:4TWY4GGRnew · submitted 2013-08-30 · 🧮 math.CO

Deterministic bootstrap percolation in high dimensional grids

Hao Huang , Choongbum Lee This is my paper
classification 🧮 math.CO
keywords bootstrappercolationconfirmsconjectured-dimensionaldeterministicdimensionalgrid
0
0 comments X
read the original 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 not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Smallest percolating sets in bootstrap percolation on grids

    math.CO 2019-07 unverdicted novelty 8.0

    The size of the smallest percolating sets in d-neighbour bootstrap percolation on [n]^d is n^{d-1} for all d ≥ 1, with percolation time at most c_d n^2.