L^2-spectral invariants and convergent sequences of finite graphs

TL;DR

This paper explores the spectral properties of sequences of finite graphs and establishes the uniform existence of the integrated density of states for a broad class of infinite graphs using spectral theory.

Contribution

It introduces a novel approach to analyze spectral invariants in weakly convergent graph sequences and proves the existence of the integrated density of states in this context.

Findings

Established uniform existence of the integrated density of states

Applied spectral theory to weakly convergent graph sequences

Extended spectral invariants to infinite graphs

Abstract

Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.