论文标题
在Poisson-Voronoi Tessellation中Delaunay邻居的角度条件下定义的点过程
On Point Processes Defined by Angular Conditions on Delaunay Neighbors in the Poisson-Voronoi Tessellation
论文作者
论文摘要
考虑欧几里得平面的均匀泊松点过程及其Voronoi Tessellation。本说明讨论了与后者相关的两个固定点过程的属性，并取决于参数$θ$。第一个是属于Voronoi Tessellation的某个一维方面的一组点，因此他们看到两个核定义该构的角度为$θ$。在第一个点过程中，兴趣的主要问题是其强度。第二点过程是所述缝线与具有随机取向的直线的相互作用的过程。它的强度是众所周知的。交点点几乎肯定属于一维相。这里的主要问题是关于第二个点过程的角度的角度的棕榈分布，请参见与该小方相关的两个核。该注释给出了这两个问题的答案，并简要讨论了他们的实际动机。它还讨论了第三维的自然扩展。
Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $θ$. The first one is the set of points that belong to some one-dimensional facet of the Voronoi tessellation and are such that the angle with which they see the two nuclei defining the facet is $θ$. The main question of interest on this first point process is its intensity. The second point process is that of the intersections of the said tessellation with a straight line having a random orientation. Its intensity is well known. The intersection points almost surely belong to one-dimensional facets. The main question here is about the Palm distribution of the angle with which the points of this second point process see the two nuclei associated with the facet. The note gives answers to these two questions and briefly discusses their practical motivations. It also discusses natural extensions to dimension three.
