论文标题
一类各向异性泊松线条的三角形的比例
The proportion of triangles in a class of anisotropic Poisson line tessellations
论文作者
论文摘要
研究了飞机中线的固定泊松过程，其方向分布集中在$ k \ ge 3 $上均等传播方向上。此类过程的随机线将平面分解成一个随机多边形的集合，该多边形形成了所谓的泊松线条。本文的重点是确定这种缝线中三角形的比例，或等效地，典型细胞是三角形的概率。作为副产品，通过近似参数获得了各向同性病例的Miles经典结果的新偏差。
Stationary Poisson processes of lines in the plane are studied whose directional distributions are concentrated on $k \ge 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently, the probability that the typical cell is a triangle. As a by-product, a new deviation of Miles' classical result for the isotropic case is obtained by an approximation argument.
