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16 - Uniform Existence of the IDS on Lattices and Groups
- By C. Schumacher, F. Schwarzenberger, I. Veselić
Edited by Matthias Keller, Universität Potsdam, Germany, Daniel Lenz, Universität Potsdam, Germany, Radoslaw K. Wojciechowski
Book:

Analysis and Geometry on Graphs and Manifolds

Published online:

14 August 2020

Print publication:

20 August 2020, pp 445-478
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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.

Integrated density of states for random metrics on manifolds
Daniel Lenz, Norbert Peyerimhoff, Ivan Veselić
Journal:

Proceedings of the London Mathematical Society / Volume 88 / Issue 3 / May 2004

Published online by Cambridge University Press:

14 April 2004, pp. 733-752

Print publication:

May 2004
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We study ergodic random Schrödinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties, the existence of a self-averaging integrated density of states and a Pastur–šubin type trace formula.

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2 results

16 - Uniform Existence of the IDS on Lattices and Groups

Summary

Integrated density of states for random metrics on manifolds