Continuity of percolation probability on hyperbolic graphs

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Abstract

Let Tk be a forwarding tree of degree k where each vertex other than the origin has k children and one parent and the origin has k children but no parent (k ≥ 2). Define G to be the graph obtained by adding to Tk nearest neighbor bonds connecting the vertices which are in the same generation. G is regarded as a discretization of the hyperbolic plane H2 in the same sense that Zd is a discretization of Rd. Independent percolation on G has been proved to have multiple phase transitions. We prove that the percolation probability 0(p) is continuous on [0,1] as a function of p.

Original languageEnglish (US)
Pages (from-to)909-913
Number of pages5
JournalJournal of Statistical Physics
Volume87
Issue number3-4
DOIs
StatePublished - May 1997

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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