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Monotonicity and phase diagram for multirange percolation on oriented trees
Author(s) -
de Lima Bernardo N. B.,
Rolla Leonardo T.,
Valesin Daniel
Publication year - 2019
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20805
Subject(s) - bernoulli's principle , percolation (cognitive psychology) , monotonic function , bond , mathematics , combinatorics , phase diagram , percolation threshold , set (abstract data type) , tree (set theory) , statistical physics , discrete mathematics , phase (matter) , computer science , physics , thermodynamics , mathematical analysis , economics , quantum mechanics , finance , neuroscience , electrical resistivity and conductivity , biology , programming language
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.