Monotonicity and phase diagram for multirange percolation on oriented trees

Bernardo N. B. de Lima*, Leonardo T. Rolla, Daniel Valesin

*Corresponding author for this work

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We consider Bernoulli bond percolation on oriented regular trees, where besides the usual short bonds, all bonds of a certain length are added. Independently, short bonds are open with probability p and long bonds are open with probability q. We study properties of the critical curve which delimits the set of pairs (p,q) for which there are almost surely no infinite paths. We also show that this curve decreases with respect to the length of the long bonds.

Original languageEnglish
Pages (from-to)160-172
Number of pages13
JournalRandom structures & algorithms
Issue number1
Publication statusPublished - Aug-2019


  • critical curve
  • long range percolation
  • monotonicity of connectivity

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