2012/04/22 by Péter Gács, Peter Gacs, Gacs, Peter
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.1204.4897
49 pages. Some errors corrected. arXiv admin note: substantial text overlap with arXiv:math/0109152
openalex publication_date 2012/04/22 · arxiv created 2014/03/21 · arxiv updated 2014/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let v, w be infinite 0-1 sequences, and m a positive integer. We say that w is m-embeddable in v, if there exists an increasing sequence ni of integers with n0=0, such that 0< ni - ni-1 < m, w(i) = v(ni) for all i > 0. Let X and Y be independent coin-tossing sequences. We will show that there is an m with the property that Y is m-embeddable into X with positive probability. This answers a question that was open for a while. The proof generalizes somewhat the hierarchical method of an earlier paper of the author on dependent percolation.