Scaling of the distribution of shortest paths in percolation
arXiv:cond-mat/9908435 · doi:10.1023/B:JOSS.0000033244.13545.da
Abstract
We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence of this distribution on the site occupancy probability $p$. We test the hypothesis for the case of two-dimensional percolation.
7 pages, 3 figures