Abstract
LetT k 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 toT k nearest neighbor bonds connecting the vertices which are in the same generation.G is regarded as a discretization of the hyperbolic planeH 2 in the same sense thatZ d is a discretization ofR d. 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.
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Communicated by T. Kennedy
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Wu, C.C. Continuity of percolation probability on hyperbolic graphs. J Stat Phys 87, 909–913 (1997). https://doi.org/10.1007/BF02181251
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DOI: https://doi.org/10.1007/BF02181251