具有纯点动力谱的一致离散点过程的灭绝与关联
Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra
摘要：
本文研究了相关性如何完全指定一个一致离散点过程。的设置是一致的离散点集在实空间中的相应的动力壳是遍历的。第一个结果是，在这样一个系统中，所有的基本物理信息都可以从它的$n$ -点相关性$n= 2, 3, >...$导出。如果系统是纯点衍射的，则所需相关数的上限可以从由动力学谱和布拉格谱形成的图的周期结构导出。特别地，如果衍射没有衍射，则2点和3点相关包含所有相关信息。
英文摘要：
The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is that all of the essential physical information in such a system is derivable from its $n$-point correlations, $n= 2, 3, >...$. If the system is pure point diffractive an upper bound on the number of correlations required can be derived from the cycle structure of a graph formed from the dynamical and Bragg spectra. In particular, if the diffraction has no extinctions, then the 2 and 3 point correlations contain all the relevant information.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
