Scaling of the distribution of shortest paths in percolation
Nikolay V. Dokholyan, Youngki Lee, Sergey V. Buldyrev, Shlomo Havlin, Peter R. King, H. Eugene Stanley
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 (i) the effect of the finite size of the system, and (ii) the dependence of this distribution on the site occupancy probability p. We test the hypothesis for the case of two-dimensional percolation.
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