Journal article

### Line-of-sight percolation

Abstract:

Given $\omega\ge 1$, let $Z^2_{(\omega)}$ be the graph with vertex set $Z^2$ in which two vertices are joined if they agree in one coordinate and differ by at most $\omega$ in the other. (Thus $Z^2_{(1)}$ is precisely $Z^2$.) Let $p_c(\omega)$ be the critical probability for site percolation in $Z^2_{(\omega)}$. Extending recent results of Frieze, Kleinberg, Ravi and Debany, we show that $\lim_{\omega\to\infty} \omega\pc(\omega)=\log(3/2)$. We also prove analogues of this result on the $n$-by...

Publication status:
Published

### Access Document

Publisher copy:
10.1017/S0963548308009310

### Authors

Journal:
Combinatorics, Probability and Computing 18 (2009), 83--106.
Volume:
18
Issue:
1-2
Pages:
83-106
Publication date:
2007-02-02
DOI:
EISSN:
1469-2163
ISSN:
0963-5483
URN:
uuid:98454460-37a6-41ce-a92f-fd7af17f8b4d
Source identifiers:
18136
Local pid:
pubs:18136
Language:
English
Keywords: