Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random fields on model sets with localized dependency and their
  diffraction   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 omega defined on the model set Lambda that satisfies
a natural geometric condition, we develop a method to calculate the diffraction
measure of the random field. The method partitions the random field into a
finite number of random fields, each being independent and admitting the law of
large numbers. The diffraction measure of omega consists almost surely of a
pure-point component and an absolutely continuous component. The former is the
diffraction measure of the expectation E[omega], while the inverse Fourier
transform of the absolutely continuous component of omega turns out to be a
weighted Dirac comb which satisfies a simple formula. Moreover, the pure-point
component will be understood quantitatively in a simple exact formula if the
weights are continuous over the internal space of Lambda Then we provide a
sufficient condition that the diffraction measure of a random field on a model
set is still pure-point.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph