Translator Disclaimer
December 2011 Percolation of words on Zd with long-range connections
B. N. B. de Lima, R. Sanchis, R. W. C. Silva
Author Affiliations +
J. Appl. Probab. 48(4): 1152-1162 (December 2011). DOI: 10.1239/jap/1324046024

Abstract

Consider an independent site percolation model on Zd, with parameter p ∈ (0, 1), where all long-range connections in the axis directions are allowed. In this work we show that, given any parameter p, there exists an integer K(p) such that all binary sequences (words) ξ ∈ {0, 1}N can be seen simultaneously, almost surely, even if all connections with length larger than K(p) are suppressed. We also show some results concerning how K(p) should scale with p as p goes to 0. Related results are also obtained for the question of whether or not almost all words are seen.

Citation

Download Citation

B. N. B. de Lima. R. Sanchis. R. W. C. Silva. "Percolation of words on Zd with long-range connections." J. Appl. Probab. 48 (4) 1152 - 1162, December 2011. https://doi.org/10.1239/jap/1324046024

Information

Published: December 2011
First available in Project Euclid: 16 December 2011

zbMATH: 1231.60118
MathSciNet: MR2896673
Digital Object Identifier: 10.1239/jap/1324046024

Subjects:
Primary: 60K35
Secondary: 82B41 , 82B43

Keywords: Percolation of words , truncation question

Rights: Copyright © 2011 Applied Probability Trust

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 4 • December 2011
Back to Top