Clusters in middle-phase percolation on hyperbolic plane

@article{JanCzajkowski2011,
abstract = {I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. $0 < p_c(G) < p_u(G) < 1$, where $p_c$ is the critical probability and $p_u$-the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].},
author = {Jan Czajkowski},
journal = {Banach Center Publications},
keywords = {percolation; hyperbolic plane; Bernoulli bond; planar graphs; phases of percolation; nonamenable graphs},
language = {eng},
number = {1},
pages = {99-113},
title = {Clusters in middle-phase percolation on hyperbolic plane},
url = {http://eudml.org/doc/282008},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Jan Czajkowski
TI - Clusters in middle-phase percolation on hyperbolic plane
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 99
EP - 113
AB - I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. $0 < p_c(G) < p_u(G) < 1$, where $p_c$ is the critical probability and $p_u$-the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].
LA - eng
KW - percolation; hyperbolic plane; Bernoulli bond; planar graphs; phases of percolation; nonamenable graphs
UR - http://eudml.org/doc/282008
ER -