The existence of an intermediate phase for the contact process on trees
成果类型：
Article
署名作者：
Stacey, AM
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1996
页码：
1711-1726
关键词：
摘要：
Let T-d be a homogeneous tree in which every vertex has d neighbors. A new proof is given that the contact process on T-d exhibits two phase transitions when d greater than or equal to 3, a behavior which distinguishes it from the contact process on Z(n). This is the first proof which does not involve calculation of bounds on critical values, and it is much shorter than the previous proof for the binary tree, T-3. The method is extended to prove the existence of an intermediate phase for a more general class of trees with exponential growth and certain symmetry properties, for which no such result was previously known.