Open Access
October 1996 The existence of an intermediate phase for the contact process on trees
A. M. Stacey
Ann. Probab. 24(4): 1711-1726 (October 1996). DOI: 10.1214/aop/1041903203


Let $\mathbb{T}_d$ be a homogeneous tree in which every vertex has $d$ neighbors. A new proof is given that the contact process on $\mathbb{T}_d$ exhibits two phase transitions when $d \geq 3$, a behavior which distinguishes it from the contact process on $\mathbb{Z}^n$. 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, $\mathbb{T}_3$. 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.


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A. M. Stacey. "The existence of an intermediate phase for the contact process on trees." Ann. Probab. 24 (4) 1711 - 1726, October 1996.


Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0878.60061
MathSciNet: MR1415226
Digital Object Identifier: 10.1214/aop/1041903203

Primary: 60K35

Keywords: contact process , multiple phase transition , tree

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 4 • October 1996
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