Authors
Citation
I. Vardi, Deterministic percolation, COMM MATH P, 207(1), 1999, pp. 43-66
Citations number
51
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616
→ ACNP
Volume
207
Issue
1
Year of publication
1999
Pages
43 - 66
Database
ISI
SICI code
0010-3616(199911)207:1<43:DP>2.0.ZU;2-K
Abstract
This paper examines percolation questions in a deterministic setting. In pa
rticular, I consider R, the set of elements of Z(2) with greatest common di
visor equal to 1, where two Sites are connected if they are at distance 1.
The main result of the paper proves that the infinite component has an asym
ptotic density. An "almost everywhere" sieve of J. Friedlander is used to o
btain the result.