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Journal of Statistical Physics

, Volume 164, Issue 1, pp 166–173 | Cite as

Truncated Long-Range Percolation on Oriented Graphs

  • A. C. D. van Enter
  • B. N. B. de LimaEmail author
  • D. Valesin
Article

Abstract

We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process.

Keywords

Contact processes Oriented percolation Long-range percolation Truncation 

Mathematics Subject Classification

60K35 82B43 

Notes

Acknowledgments

This work was done during B.N.B.L.’s sabbatical stay at IMPA; he would like to thank Rijksuniversiteit Groningen and IMPA for their hospitality. The research of B.N.B.L. was supported in part by CNPq and FAPEMIG (Programa Pesquisador Mineiro).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Johann Bernoulli InstituutRijksuniversiteit GroningenGroningenThe Netherlands
  2. 2.Departamento de MatemáticaUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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