Monotonicity and phase diagram for multirange percolation on oriented trees

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...

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Bibliographic Details
Published in:Random structures & algorithms 2019-08, Vol.55 (1), p.160-172
Main Authors: de Lima, Bernardo N. B., Rolla, Leonardo T., Valesin, Daniel
Format: Article
Language:English
Subjects:
Bonding
critical curve
long range percolation
monotonicity of connectivity
Percolation
Phase diagrams
Polytrees
Trees (mathematics)
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Summary: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.
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20805