Year: 2024
Type: preprint
Abstract: We consider the $r$-neighbor bootstrap percolation process on the graph with vertex set $V=\{0,1\}^n$ and edges connecting the pairs at Hamming distance $1,2,\dots,k$, where $k\ge 2$. We find asymptotics of the critical probability of percolation for $r=2,3$. In the deterministic setting, we obtain several results for the size of the smallest percolating set for $k\ge 2$.
Source: arXiv (Cornell University)
Author: Zhu, Fengxing
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4405957573