# Uniform existence of the IDS on lattices and groups

## TL;DR

This paper develops a general framework for thermodynamic limits in lattice and group models, establishing criteria for uniform convergence, exemplified by eigenvalue counting functions converging uniformly to the integrated density of states.

## Contribution

It introduces a unified approach to thermodynamic limits with conditions ensuring uniform convergence across parameters, applied to spectral analysis.

## Key findings

- Criteria for uniform thermodynamic limits established
- Eigenvalue counting functions converge uniformly to the IDS
- Framework applicable to various lattice and group models

## Abstract

We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter. All results are illustrated with the example of eigenvalue counting functions converging to the integrated density of states. In this case, the convergence is uniform in the energy.

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Source: https://tomesphere.com/paper/1901.08834