# Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra - Mathematical Physics

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Abstract: The paper investigates how correlations can completely specify a uniformlydiscrete point process. The setting is that of uniformly discrete point sets inreal space for which the corresponding dynamical hull is ergodic. The firstresult is that all of the essential physical information in such a system isderivable from its $n$-point correlations, $n= 2, 3, >

.$. If the system ispure point diffractive an upper bound on the number of correlations requiredcan be derived from the cycle structure of a graph formed from the dynamicaland Bragg spectra. In particular, if the diffraction has no extinctions, thenthe 2 and 3 point correlations contain all the relevant information.

Author: ** Daniel Lenz, Robert V. Moody**

Source: https://arxiv.org/