Harmonic models and spanning forests of residually finite groups

TL;DR

This paper establishes new identities linking sofic entropy, Wired Spanning Forest entropy, and tree entropy in residually finite groups, and demonstrates the density of homoclinic and periodic points in harmonic models.

Contribution

It introduces novel relationships between different entropy measures and harmonic models in residually finite groups, expanding understanding of their dynamical properties.

Findings

Identities relating sofic entropy, Wired Spanning Forest entropy, and tree entropy.

Density of homoclinic and periodic points in harmonic models.

Connections between algebraic dynamical systems and graph entropy measures.

Abstract

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.