随机点上的连通空间网络与路径长度统计
Connected Spatial Networks over Random Points and a Route-Length Statistic
摘要：
我们审查数学上听话的模型连接网络的随机点在平面上，强调类的邻近图，值得更好地了解应用probabilists和统计学家。我们介绍和激励一个特定的统计$R$测量在网络中的路由短。我们说明，通过蒙特卡罗的一部分，归一化网络长度和$R$之间的权衡在一个参数的家庭的邻近图。这个家庭如何接近所有可能的网络的最佳权衡仍然是一个有趣的开放问题。本文是第一作者在2007- 2009年期间的一次演讲的总结。
英文摘要：
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate a particular statistic $R$ measuring shortness of routes in a network. We illustrate, via Monte Carlo in part, the trade-off between normalized network length and $R$ in a one-parameter family of proximity graphs. How close this family comes to the optimal trade-off over all possible networks remains an intriguing open question. The paper is a write-up of a talk developed by the first author during 2007--2009.
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