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April 1998 Limit set of a weakly supercritical contact process on a homogeneous tree
Steven P. Lalley, Tom Sellke
Ann. Probab. 26(2): 644-657 (April 1998). DOI: 10.1214/aop/1022855646

Abstract

A conjecture of Liggett concerning the regime of weak survival for the contact process on a homogeneous tree is proved. The conjecture is shown to imply that the Hausdorff dimension of the limit set of such a contact process is no larger than half the Hausdorff dimension of the space of ends of the tree. The conjecture is also shown to imply that at the boundary between weak survival and strong survival, the contact process survives only weakly, a theorem previously proved by Zhang. Finally, a stronger form of a theorem of Hawkes and Lyons concerning the Hausdorff dimension of a Galton–Watson tree is proved.

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Steven P. Lalley. Tom Sellke. "Limit set of a weakly supercritical contact process on a homogeneous tree." Ann. Probab. 26 (2) 644 - 657, April 1998. https://doi.org/10.1214/aop/1022855646

Information

Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0937.60093
MathSciNet: MR1626499
Digital Object Identifier: 10.1214/aop/1022855646

Subjects:
Primary: 60K35

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 1998
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