论文标题
关于平面泊松线过程的面积和周长的分布功能
On the Distribution function of area and perimeter for planar poisson line process
论文作者
论文摘要
检查空间随机分区的挑战是几何转化理论中的一系列重要问题。理查德·迈尔斯（Richard Miles）计算了1972年空间随机划分的任何顺序（包括期望）的区域和周围的力矩。在本文中，我们通过泊松线过程计算了平面随机分裂的整个分布函数。 这个想法是将随机多边形解释为沿移动直线的段的演变。在平面示例中，通过考虑割线线来克服与无限数量参数相关的问题。 我们将考虑以下任务： {\ textbf 1.}在平面上，提供了一组直线，所有偏移均可能同样可能，并且分布定律的形式为$ f（φ）。$ $什么是分区组件的面积分布？ {\ textbf 2.}在平面上，标记了一组随机的点。每个点$ a $都有一个关联的吸引力区域，这是平面中点$ a $的点的集合。 在第一个问题中，与线相邻的移动部分的密度允许以动力学形式表达平衡比。同样，您可以编写周长动力学方程。 我们将使用本文中的拉普拉斯转换来演示如何将这些方程式减少到riccati方程。
The challenges of examining random partitions of space are a significant class of problems in the theory of geometric transformations. Richard Miles calculated moments of areas and perimeters of any order (including expectation) of the random division of space in 1972. In the paper we calculate whole distribution function of random divisions of plane by poisson line process. The idea is to interpret a random polygon as the evolution of a segment along a moving straight line. In the plane example, the issue connected with an infinite number of parameters is overcome by considering a secant line. We shall take into account the following tasks: {\textbf 1.} On the plane, a random set of straight lines is provided, all shifts are equally likely, and the distribution law is of the form $F(φ).$ What is the area distribution of the partition's components? {\textbf 2.} On the plane, a random set of points is marked. Each point $A$ has an associated area of attraction, which is the collection of points in the plane to which the point $A$ is the nearest of the designated ones. In the first problem, the density of moved sections adjacent to the line allows for the expression of the balancing ratio in kinetic form. Similarly, you can write the perimeters kinetic equations. We will demonstrate how to reduce these equations to the Riccati equation using the Laplace transformation in this paper.
