Compatible sequences and a slow Winkler percolation
OA Version
Citation
P Gacs. 2004. "Compatible sequences and a slow Winkler percolation." Combinatorics, Probability and Computing, Volume 13, Issue 6, pp. 815 - 856 (42). https://doi.org/10.1017/S0963548304006340
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 behaviour: the probability that the origin is blocked at distance $n$ but not closer decreases only polynomially fast and not, as usual, exponentially.