Uniform existence of the IDS on lattices and groups

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.

30 pages, 6 figures, proceedings of the conference Analysis and Geometry on Graphs and Manifolds 2017 at the University of Potsdam