Abstract
The contact process on a homogeneous tree of degree 3 or larger is known to have two survival phases: weak and strong. In the weak survival phase, the (the Hausdorff dimension of the set of ends of the tree in which the infection survives) is less than half the Hausdorff dimension of the entire boundary. It is shown that if the expected infection time of a vertex is bounded by a constant times the probability of infection, then the critical exponent for the Malthusian parameter is at least 1/2.
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