Monotonicity and phase diagram for multirange percolation on oriented trees

Bernardo N. B. de Lima; Leonardo T. Rolla; Daniel Valesin

doi:10.1002/rsa.20805

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

Probability and Statistics

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

86 Downloads (Pure)

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.

Original language	English
Pages (from-to)	160-172
Number of pages	13
Journal	Random structures & algorithms
Volume	55
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20805
Publication status	Published - Aug-2019

Keywords

critical curve
long range percolation
monotonicity of connectivity

Access to Document

10.1002/rsa.20805

Monotonicity and phase diagram for multirangepercolation on oriented treesFinal publisher's version, 343 KBLicence: Taverne

http://arxiv.org/pdf/1702.03841Licence: Unspecified

Handle.net

Persistent link

Cite this

@article{a9c8c4188e7041cab99341c2f31b206c,

title = "Monotonicity and phase diagram for multirange percolation on oriented trees",

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.",

keywords = "critical curve, long range percolation, monotonicity of connectivity",

author = "{de Lima}, {Bernardo N. B.} and Rolla, {Leonardo T.} and Daniel Valesin",

year = "2019",

month = aug,

doi = "10.1002/rsa.20805",

language = "English",

volume = "55",

pages = "160--172",

journal = "Random structures & algorithms",

issn = "1042-9832",

publisher = "Wiley",

number = "1",

}

TY - JOUR

T1 - Monotonicity and phase diagram for multirange percolation on oriented trees

AU - de Lima, Bernardo N. B.

AU - Rolla, Leonardo T.

AU - Valesin, Daniel

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

KW - critical curve

KW - long range percolation

KW - monotonicity of connectivity

U2 - 10.1002/rsa.20805

DO - 10.1002/rsa.20805

M3 - Article

SN - 1042-9832

VL - 55

SP - 160

EP - 172

JO - Random structures & algorithms

JF - Random structures & algorithms

IS - 1

ER -

Monotonicity and phase diagram for multirange percolation on oriented trees

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this