Percolation of arbitrary words in one dimension

Details Percolation of arbitrary words in one dimension Percolation of arbitrary words in one dimension

2008-07-10

arxiv.org/abs/0807.1676v1

Mathematics

Probability

16 pages

Scientific paper

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.

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