论文标题
在实际双曲空间和固定点过程中的Delaunay复合物的锚定扩展
Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes
论文作者
论文摘要
我们为在任何维真实双曲空间中的离散点提供足够的条件，以具有正锚固的膨胀。第一个条件是有界的平均密度属性，确保在大区域内不会积聚太多点。第二个是一个有界的平均空缺条件，有效地确保了在大区域上没有太多空间。这些特性给出了一个简单的推论，即固定的泊松 - delaunay图具有正锚的伸展，以及由固定确定点过程构建的Delaunay图。 我们介绍了一个固定确定点过程的家族，上面是实际双曲线空间，贝雷嗪点过程的任何维度，我们部分对它们进行了表征。我们提出了许多与此过程和固定确定点过程有关的问题。
We give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is a bounded mean density property, ensuring not too many points can accumulate in large regions. The second is a bounded mean vacancy condition, effectively ensuring there is not too much space left vacant by the points over large regions. These properties give as an easy corollary that stationary Poisson--Delaunay graphs have positive anchored expansion, as well as Delaunay graphs built from stationary determinantal point processes. We introduce a family of stationary determinantal point processes on any dimension of real hyperbolic space, the Berezin point processes, and we partially characterize them. We pose many questions related to this process and stationary determinantal point processes.
