Compatible sequences and a slow Winkler percolation

Peter Gacs

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Compatible sequences and a slow Winkler percolation

Peter Gacs

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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.

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BibTeX RIS

Peter Gacs. 2003-01-18. Compatible sequences and a slow Winkler percolation. https://arxiv.org/abs/math/0011008

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