Improper poisson line process as sirsn in any dimension
Improper poisson line process as sirsn in any dimension
复制标题
任何维度上的不当泊松线过程
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Kahn
中科院分区：
文献类型：
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作者：
J. Kahn
Aldous引入了尺度不变随机空间网络（SIRSN）的概念，作为道路网络的数学形式化。直观地说，这些是随机过程，在欧几里得空间中的每对点之间分配路线，同时在旋转，平移和尺度变化下不变，并且使得路线不会太长并且主要在“主干道”上。唯一已知的例子是有点人为的，因为不变性必须添加在建设结束。我们证明了网络的测地线在随机度量空间中产生的泊松线过程标记的速度根据幂律是一个SIRSN，在任何维度。沿着的方式，我们建立界限比较欧几里德球和球的随机度量空间。我们还证明，在二维以上，测地线有“许多方向”附近的每个点，他们不是直的。
Aldous has introduced a notion of scale-invariant random spatial network (SIRSN) as a mathematical formalization of road networks. Intuitively, those are random processes that assign a route between each pair of points in Euclidean space, while being invariant under rotation, translation, and change of scale, and such that the routes are not too long and mainly on "main roads". The only known example was somewhat artificial since invariance had to be added at the end of the construction. We prove that the network of geodesics in the random metric space generated by a Poisson line process marked by speeds according to a power law is a SIRSN, in any dimension. Along the way, we establish bounds comparing Euclidean balls and balls for the random metric space. We also prove that in dimension more than two, the geodesics have "many directions" near each point where they are not straight.
从随机线到度量空间
DOI：
10.1214/14-aop935
发表时间：
2017
期刊：
The Annals of Probability
影响因子：
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作者：
Kendall W
通讯作者：
Kendall W