Clusters in middle-phase percolation on hyperbolic plane

• Autorzy: Jan Czajkowski
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 20H10: Fuchsian groups and their generalizations
• 60K35: Interacting random processes; statistical mechanics type models; percolation theory
• 82B43: Percolation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 99-113

Daty

wydano

2011

Twórcy

autor

Jan Czajkowski

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc96-0-6