# Clusters in middle-phase percolation on hyperbolic plane

Banach Center Publications (2011)

- Volume: 96, Issue: 1, page 99-113
- ISSN: 0137-6934

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topJan Czajkowski. "Clusters in middle-phase percolation on hyperbolic plane." Banach Center Publications 96.1 (2011): 99-113. <http://eudml.org/doc/282008>.

@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 -

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