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• W1648177587 abstract "The existence of a weak survival region is established for the anisotropic symmetric contact process on a homogeneous tree T2d of degree 2d ≥ 4 : For parameter values in a certain connected region of positive Lebesgue measure, the population survives forever with positive probability but ultimately vacates every finite subset of the tree with probability one. In this phase, infection trails must converge to the geometric boundary of the tree. The random subsetof the boundary consisting of all ends of the tree in which the infection survives, called the limit set of the process, is shown to have Hausdorff dimension no larger than one half the Hausdorff dimension of the entire geometric boundary. In addition, there is strict inequality at the transition between weak and strong survival except when the contact process is isotropic. It is further shown that in all cases there is a distinguished probability measure �, supported by , such that the Hausdorff dimension of � ∩µ, where µ is the set of � -generic points of , converges to one half the Hausdorff dimension of µ at the phase separation points. Exact formulae for the Hausdorff dimensions ofand � ∩ µ are obtained. We also prove that the contact process at the transition between extinction and weak survival does not survive. The method developed shows that the contact process at the phase transition to strong survival survives weakly for d ≥ 2." @default.
• W1648177587 created "2016-06-24" @default.
• W1648177587 creator A5065358578 @default.
• W1648177587 date "2001-09-06" @default.
• W1648177587 modified "2023-09-27" @default.
• W1648177587 title "ANISOTROPIC CONTACT PROCESS ON HOMOGENEOUS TREES" @default.
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• W1648177587 hasPublicationYear "2001" @default.
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