Journal of Statistical Physics

, Volume 87, Issue 3–4, pp 909–913 | Cite as

Continuity of percolation probability on hyperbolic graphs

  • C. Chris Wu
Short Communications

Abstract

LetTk be a forwarding tree of degreek where each vertex other than the origin hask children and one parent and the origin hask children but no parent (k≥2). DefineG to be the graph obtained by adding toTk nearest neighbor bonds connecting the vertices which are in the same generation.G is regarded as a discretization of the hyperbolic planeH2 in the same sense thatZd is a discretization ofRd. Independent percolation onG has been proved to have multiple phase transitions. We prove that the percolation probabilityO(p) is continuous on [0,1] as a function ofp.

Key Words

Percolation percolation probability hyperbolic graphs 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • C. Chris Wu
    • 1
  1. 1.Department of MathematicsPenn State UniversityMonaca

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