Threshold phenomena for the anisotropic contact process.
Preprint (March 2001)

This paper reviews results on the isotropic contact process on an infinite homogeneous tree and selected results of work of Hueter on the symmetric anisotropic process on T_2d for 2d > 2, while it is also meant to serve as a friendly guide through some ideas of the approach taken in Hueter that borrows a collection of tools from dynamical system and carries further an analogy between the contact process and the random walk on T_2d. One goal is to gain insight into the picture of explosion of the symmetric anisotropic contact process at the weak/strong survival threshold, which may be quantified by saying that, at this threshold, the critical exponent of the log of the expected size of the set of all infected ends of the tree does not exceed 1/2, with equality 1/2 holding if and only if the process is isotropic. We end with a discussion of the contact process on less regular trees, on subperiodic trees, and with a number of open problems.