Limit set of a weakly supercritical contact process on a homogeneous tree
成果类型：
Article
署名作者：
Lalley, SP; Sellke, T
署名单位：
Purdue University System; Purdue University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1998
页码：
644-657
关键词：
摘要：
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.