Abstract
Let T~ be a Ibrwarding 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 T~ nearest neighbor bonds connecting the vertices which are in the same generation. G is regarded as a discretization of the hyperbolic plane H'- in the same sense that Z a is a discretization of R a. Independent percolation on G has been proved to have multiple phase transitions. We prove that the percolation probability (l(p) is continuous on [0.1 ] as a function ofp.
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