Boundary representation of Dirichlet forms on discrete spaces

TL;DR

This paper characterizes all Dirichlet forms on an infinite graph using boundary forms, providing an analytical framework that links graph structures to boundary behavior.

Contribution

It introduces a novel boundary representation for Dirichlet forms on infinite graphs using purely analytical methods.

Findings

Complete characterization of Dirichlet forms via boundary forms

Analytical approach using form methods

Framework applicable to infinite graphs

Abstract

We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods.