Uniform existence of the integrated density of states for models on $${\mathbb{Z}}^d$$ |
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Authors: | Daniel Lenz Peter Müller Ivan Veseli? |
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Institution: | 1.Fakult?t für Mathematik,Chemnitz,Germany;2.Institut für Theoretische Physik,G?ttingen,Germany;3.Emmy-Noether-Programme of the Deutsche Forschungsgemeinschaft & Fakult?t für Mathematik,TU Chemnitz,Germany |
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Abstract: | We provide an ergodic theorem for certain Banach-space valued functions on structures over , which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density
of states for associated discrete finite-range operators in the sense of convergence of the distributions with respect to
the supremum norm. These results apply to various examples including periodic operators, percolation models and nearest-neighbour
hopping on the set of visible points. Our method gives explicit bounds on the speed of convergence in terms of the speed of
convergence of the underlying frequencies. It uses neither von Neumann algebras nor a framework of random operators on a probability
space.
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Keywords: | Random Schr?dinger operator integrated density of states uniform ergodic theorem |
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