2009/05/28 by Bernardo N. B. de Lima, de Lima, Bernardo N. B., Rémy Sanchis +4
Mathematics · Physics and Astronomy · #60K35 #82B41 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60K35 #msc:82B41 #msc:82B43
paper · pdf · doi:10.48550/arxiv.0905.4615
10 pages, without figures
arxiv created 2009/05/28 · openalex publication_date 2009/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an independent site percolation model on \Zd, with parameter p ∈ (0,1), where all long range connections in the axes directions are allowed. In this work we show that given any parameter p, there exists and integer K(p) such that all binary sequences (words) ξ∈ \0,1\\N can be seen simultaneously, almost surely, even if all connections whose length is bigger than K(p) are suppressed. We also show some results concerning the question how K(p) should scale with p when p goes to zero. Related results are also obtained for the question of whether or not almost all words are seen.