Compatible sequences and a slow Winkler percolation
Probability
2009-09-25 v5 Combinatorics
Abstract
Two infinite 0-1 sequences are called compatible when it is possible to cast out 0's from both in such a way that they become complementary to each other. Answering a question of Peter Winkler, we show that if the two 0-1-sequences are random i.i.d. and independent from each other, with probability p of 1's, then if p is sufficiently small they are compatible with positive probability. The question is equivalent to a certain dependent percolation with a power-law behavior: the probability that the origin is blocked at distance n but not closer decreases only polynomially fast and not, as usual, exponentially.
Cite
@article{arxiv.math/0011008,
title = {Compatible sequences and a slow Winkler percolation},
author = {Peter Gacs},
journal= {arXiv preprint arXiv:math/0011008},
year = {2009}
}
Comments
33 pages, 8 figures. Submitted to Combinatorics, Probability and Computing. Some errors corrected