Monotonicity and phase diagram for multirange percolation on oriented trees. Issue 1 (15th October 2018)

• Record Type: Journal Article
• Authors: de Lima, Bernardo N. B.; Rolla, Leonardo T.; Valesin, Daniel
• Is Part Of: Random structures & algorithms. Volume 55:Issue 1(2019)
• Page Start: 160
• Page End: 172
• Publication Date: 2018-10-15
• Subjects: critical curve -- long range percolation -- monotonicity of connectivity; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20805
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : 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.