Percolation of arbitrary words in one dimension

We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and provide partial results in others.

• Type: Journal
• Year: 2010
• Where: RSA
• Authors: Geoffrey R. Grimmett, Thomas M. Liggett, Thomas Richthammer
• Keywords: Iid Bernoulli Sequence, Long-range Percolation Problem, RSA 2010, Site Percolation Model