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Scaling of the Distribution of Shortest Paths in Percolation |
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| Authors: | Nikolay V. Dokholyan Youngki Lee Sergey V. Buldyrev Shlomo Havlin Peter R. King H. Eugene Stanley |
| Affiliation: | 1. Center of Polymer Studies and Physics Department, Boston University, Boston, Massachusetts, 02215 2. Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel 3. BP Exploration Operating Company Ltd., Sunbury-on-Thames, Midds., TW16 7LN, U.K 4. Department of Engineering, Cambridge University, Cambridge, U.K |
| 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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