Harmonic models and spanning forests of residually finite groups

We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups.We also show that homoclinic points and periodic points in harmonic models are dense under general conditions. © 2012 Elsevier Inc. All rights reserved