The branching random walk and contact process on Galton-Watson and nonhomogeneous trees

• 成果类型: Article
• 署名作者: Pemantle, R; Stacey, AM
• 署名单位: University System of Ohio; Ohio State University; University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 1563-1590
• 关键词: extremal invariant measure; homogeneous trees; transitions; phase; set

摘要

We show that the branching random walk on a Galton-Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there are some Galton-Watson trees on which the branching random walk has one phase transition while the contact process has two; this contradicts a conjecture of Madras and Schinazi. We show that the contact process has only one phase transition on some trees of uniformly exponential growth and bounded degree, contradicting a conjecture of Pemantle.