Monotonicity and phase diagram for multirange percolation on oriented trees. Issue 1 (15th October 2018) - de Lima, Bernardo N. B.; Rolla, Leonardo T.; Valesin, Daniel
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.