The complete convergence theorem of the contact process on trees
成果类型：
Article
署名作者：
Zhang, Y
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1065725187
发表日期：
1996
页码：
1408-1443
关键词：
摘要：
Consider the contact process on a homogeneous tree with degree d greater than or equal to 3. Denote by lambda(c) = inf{lambda:P(o is an element of xi i.o.) > 0} the critical value of local survival probability, where o is the root of the tree. Pemantle and Durrett and Schinazi both conjectured that the complete convergence theorem should hold if lambda > lambda(c). Here we answer the conjecture affirmatively. Furthermore, we will show that P(o is an element of xi(t)(o) i.o.) = 0 at lambda(c). Therefore, the conclusion of the complete convergence theorem cannot hold at lambda(c).