论文标题
切割和项目集的分类和统计数据
Classification and statistics of cut and project sets
论文作者
论文摘要
我们定义了Ratner-Marklof-Strombergsson的措施。这些是在r^d（d> 1）中支持的剪切和项目集中支持的概率度量，对于组ASL_D（R）或SL_D（R）的作用而言是不变的和ergodic的。我们对代数群和均匀动力学的措施进行分类。使用分类，我们证明了Siegel，Weil和Rogers的结果类似于Siegel求和公式以及涉及更高矩的身份和边界。我们针对典型的剪切和项目集合进行了有关渐近学的结果，具有错误估计，并进行了分数计数和补丁计数。
We define Ratner-Marklof-Strombergsson measures. These are probability measures supported on cut-and-project sets in R^d (d > 1) which are invariant and ergodic for the action of the groups ASL_d(R) or SL_d(R). We classify the measures that can arise in terms of algebraic groups and homogeneous dynamics. Using the classification, we prove analogues of results of Siegel, Weil and Rogers about a Siegel summation formula and identities and bounds involving higher moments. We deduce results about asymptotics, with error estimates, of point-counting and patch-counting for typical cut-and-project sets.
