Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How model sets can be determined by their two-point and three-point
  correlations   We show that real model sets with real internal spaces are determined, up to
translation and changes of density zero by their two- and three-point
correlations. We also show that there exist pairs of real (even one
dimensional) aperiodic model sets with internal spaces that are products of
real spaces and finite cyclic groups whose two- and three-point correlations
are identical but which are not related by either translation or inversion of
their windows. All these examples are pure point diffractive.
  Placed in the context of ergodic uniformly discrete point processes, the
result is that real point processes of model sets based on real internal
windows are determined by their second and third moments.

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The categories of this paper are: astro-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin