1,826 research outputs found
Uniform existence of the integrated density of states for models on \ZZ^d
We provide an ergodic theorem for certain Banach-space valued functions on
structures over \ZZ^d, which allow for existence of frequencies of finite
patterns. As an application we obtain existence of the integrated density of
states for associated 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.Comment: 15 page
Discontinuities of the integrated density of states for random operators on Delone sets
Despite all the analogies with "usual random" models, tight binding operators
for quasicrystals exhibit a feature which clearly distinguishes them from the
former: the integrated density of states may be discontinuous. This phenomenon
is identified as a local effect, due to occurrence of eigenfunctions with
bounded support.Comment: 9 pages, 2 figure
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