Workshop on Dynamical Systems and Aperiodic Order
Bielefeld University, Germany
14th - 17th March 2011
All talks take place in Room V3-201 ("Common Room") in the Bielefeld
University main building.
Click here for
a description of the main building.
Ergodic properties of randomly coloured point sets
Christoph Richard
Abstract:
In order to analyse spectral properties of an aperiodically
ordered point set such as the vertex set of the Penrose
tiling, it has proven useful to consider the closure of the
collection of all translates of the given point set, with
respect to a suitable topology. In particular, there is a
geometric characterisation of unique ergodicity in terms
of so-called uniform pattern frequencies.
We prove such a characterisation within a generalised setup, where
we allow for a uniformly discrete point set in a locally compact
metric space and a continuous and proper action of a locally compact, metric, unimodular group, which admits suitable averaging sequences.
We will discuss applications of our setup to random colourings and
graphs.
This is joint work with Peter Müller, Munich.
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