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Infinite clusters in percolation models

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Abstract

The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown thatN 0, the number of distinct infinite clusters, is either 0, 1, or ∞ and the caseN 0=∞ (which might occur in sufficiently high dimension) is analyzed.

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Authors and Affiliations

  1. Mathematics Department, University of Arizona, 85721, Tucson, Arizona, USA

    C. M. Newman

  2. Department of Physics, Technion, Haifa, Israel

    L. S. Schulman

Authors
  1. C. M. Newman
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  2. L. S. Schulman
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Additional information

Alfred P. Sloan Research Fellow, Research supported in part by National Science Foundation grant No. MCS 77-20683 and by the U.S.-Israel Binational Science Foundation.

Research supported in part by the U.S.Israel Binational Science Foundation.

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Newman, C.M., Schulman, L.S. Infinite clusters in percolation models. J Stat Phys 26, 613–628 (1981). https://doi.org/10.1007/BF01011437

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  • DOI: https://doi.org/10.1007/BF01011437

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