临界有向正方形格上最短路的扰动
Perturbing the Shortest Path on a Critical Directed Square Lattice
摘要：
本文研究了在临界概率为$p_c$的有向二维正方晶格上键渗流的最短路径的行为。我们观察到，翻转躺在最短路径的边缘有一个非局部的影响，在幂律分布的形式，最短路径长度的差异和最小的封闭区域。使用极大似然估计和外推，我们发现的指数$α= 1.36 \pm 0.01$的路径长度差和$β= 1.186 \pm 0.001$的封闭区域。
英文摘要：
We investigate the behaviour of the shortest path on a directed two-dimensional square lattice for bond percolation at the critical probability $p_c$ . We observe that flipping an edge lying on the shortest path has a non-local effect in the form of power-law distributions for both the differences in shortest path lengths and for the minimal enclosed areas. Using maximum likelihood estimation and extrapolation we find the exponents $α= 1.36 \pm 0.01$ for the path length differences and $β= 1.186 \pm 0.001$ for the enclosed areas.
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