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Scaling of the Distribution of Shortest Paths in Percolation

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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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Authors and Affiliations

  1. Center of Polymer Studies and Physics Department, Boston University, Boston, Massachusetts, 02215

    Nikolay V. Dokholyan, Youngki Lee, Sergey V. Buldyrev & H. Eugene Stanley

  2. Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel

    Shlomo Havlin

  3. BP Exploration Operating Company Ltd., Sunbury-on-Thames, Midds., TW16 7LN, U.K

    Peter R. King

  4. Department of Engineering, Cambridge University, Cambridge, U.K

    Peter R. King

Authors
  1. Nikolay V. Dokholyan
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  2. Youngki Lee
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  3. Sergey V. Buldyrev
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  4. Shlomo Havlin
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  5. Peter R. King
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  6. H. Eugene Stanley
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Correspondence to Nikolay V. Dokholyan.

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Dokholyan, N.V., Lee, Y., Buldyrev, S.V. et al. Scaling of the Distribution of Shortest Paths in Percolation. Journal of Statistical Physics 93, 603–613 (1998). https://doi.org/10.1023/B:JOSS.0000033244.13545.da

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  • DOI: https://doi.org/10.1023/B:JOSS.0000033244.13545.da

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