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Annales Henri Poincaré

, Volume 16, Issue 4, pp 1067–1101 | Cite as

Approximation of the Integrated Density of States on Sofic Groups

  • Christoph SchumacherEmail author
  • Fabian Schwarzenberger
Article
First Online:

Abstract

In this paper, we study spectral properties of self-adjoint operators on a large class of geometries given via sofic groups. We prove that the associated integrated densities of states can be approximated via finite volume analogues. This is investigated in the deterministic as well as in the random setting. In both cases, we cover a wide range of operators including in particular unbounded ones. The large generality of our setting allows one to treat applications from long-range percolation and the Anderson model. Our results apply to operators on \({\mathbb{Z}^d}\) , amenable groups, residually finite groups and therefore in particular to operators on trees. All convergence results are established without an ergodic theorem at hand.

Keywords

Matrix Element Cayley Graph Ergodic Theorem Amenable Group Anderson Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Fakultät für MathematikTU ChemnitzChemnitzGermany

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