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.
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a description of the main building.
Epsilon-duals of model sets and diffraction measure of randomized
model sets
Yohji Akama
Abstract:
Yohji Akama(1) and Shinji Iizuka(2)
(1) Mathematical Institute, Tohoku University.
(2) Research and Development Section, Hitachi East Japan Solutions, Ltd.
By using a dynamical system, we will show following two results:
(1) Moody's epsilon dual of a model set over a cut-and-project scheme
with a window W is exactly the model set over the dual cut-and-project
scheme with the window being the epsilon-dual of W.
(2) For a random field on a general discrete set, we introduce
a condition that the range of the correlation from each
site is within a predefined compact set D. For such a
random field defined on a model set that satisfies
a natural geometric condition, we quantitatively
calculate the diffraction measure of the random field.
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