Stochastic Processes on Trees

Title: Spin models on trees

We will start with an introduction to the theory of Gibbs measures on general countable graphs, including lattices and trees.

Here we will discuss the basic important issues of uniqueness vs phase transitions, extremal Gibbs measures, and the extremal decomposition. 

In the second part we will then turn specifically to spin models on trees. Here the important notion of  tree-indexed Markov chains becomes relevant.

We discuss their relation to extremal Gibbs measures, introduce the boundary law formalism, and describe how this can be used in the analysis.