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Percolation of Words on Z d with Long-Range Connections

  • B. N. B. de Lima (a1), R. Sanchis (a1) and R. W. C. Silva (a2)

Abstract

Consider an independent site percolation model on Z d , with parameter p ∈ (0, 1), where all long-range connections in the axis directions are allowed. In this work we show that, given any parameter p, there exists an integer K(p) such that all binary sequences (words) ξ ∈ {0, 1} N can be seen simultaneously, almost surely, even if all connections with length larger than K(p) are suppressed. We also show some results concerning how K(p) should scale with p as p goes to 0. Related results are also obtained for the question of whether or not almost all words are seen.

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Copyright

Corresponding author

Postal address: Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, CP 702, CEP 30123-970 Belo Horizonte, MG, Brazil.
∗∗ Email address: rsanchis@mat.ufmg.br
∗∗∗ Postal address: Departamento de Estatística, UFMG, Av. Antônio Carlos 6627, CP 702, CEP 30123-970 Belo Horizonte, MG, Brazil.

References

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Keywords

MSC classification

Percolation of Words on Z d with Long-Range Connections

  • B. N. B. de Lima (a1), R. Sanchis (a1) and R. W. C. Silva (a2)

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