论文标题
在空的半平面中伸长泊松 - 伏罗尼元细胞
Elongated Poisson-Voronoi cells in an empty half-plane
论文作者
论文摘要
下半平面中均匀的泊松点过程的Voronoi Tessellation会导致上半平面中的垂直伸长细胞家族。这些细胞的边缘集由马尔可夫分支机理统治，该机制由两个分别是beta和指数分布的IID变量序列渐近地描述。这导致了对所谓典型单元的缩放限制的精确描述。极限对象是一个随机的apeirogon，我们将其命名为Menhir。我们还从上述分支机制中推断出，高度$λ$的顶点的数量在渐近上等于$ \ frac45 \logλ$。
The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges of these cells is ruled by a Markovian branching mechanism which is asymptotically described by two sequences of iid variables which are respectively Beta and exponentially distributed. This leads to a precise description of the scaling limit of a so-called typical cell. The limit object is a random apeirogon that we name menhir in reference to the Gallic huge stones. We also deduce from the aforementioned branching mechanism that the number of vertices of a cell of height $λ$ is asymptotically equal to $\frac45\logλ$.
