Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Department of Physics, Technion, Haifa 32000, Israel.
Phys Rev E. 2017 Nov;96(5-1):050301. doi: 10.1103/PhysRevE.96.050301. Epub 2017 Nov 1.
We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. We find that, to a good approximation, the optimal paths can be described as directed polymers in a disordered medium, which belong to the Kardar-Parisi-Zhang universality class of interface roughening. Comparing the scaling behavior of our data with simulations of directed polymers and previous theoretical results, we are able to point out the few characteristics of the road network that are relevant to the large-scale statistics of optimal paths. Indeed, we show that the local structure is akin to a disordered environment with a power-law distribution which become less important at large scales where long-ranged correlations in the network control the scaling behavior of the optimal paths.
我们分析了随机抽样终点之间道路网络上最短和最快路径的统计数据。我们发现，很好地近似，最优路径可以被描述为无序介质中的定向聚合物，这属于界面粗化的 Kardar-Parisi-Zhang 普遍类。将我们的数据的标度行为与定向聚合物的模拟和以前的理论结果进行比较，我们能够指出与最优路径的大尺度统计有关的道路网络的几个特征。事实上，我们表明，局部结构类似于具有幂律分布的无序环境，在网络中的长程相关性控制最优路径的标度行为的大尺度上，这种分布变得不那么重要。
