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16 - Uniform Existence of the IDS on Lattices and Groups

Published online by Cambridge University Press:  14 August 2020

By
C. Schumacher ,
F. Schwarzenberger  and
I. Veselić
Edited by
Matthias Keller ,
Daniel Lenz  and
Radoslaw K. Wojciechowski
Matthias Keller
Affiliation:
Universität Potsdam, Germany
Daniel Lenz
Affiliation:
Universität Potsdam, Germany
Radoslaw K. Wojciechowski
Affiliation:
York College of the City University of New York
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Summary

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.

Keywords

Fölner sequencequasi-tilingEmpirical measuresKolmogorov distanceGlivenko-Cantelli theoryintegrated density of states
Type
Chapter
Information
Analysis and Geometry on Graphs and Manifolds , pp. 445 - 478
Publisher: Cambridge University Press
Print publication year: 2020

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