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1 results

  • The Asymptotic Size of the Largest Component in Random Geometric Graphs with Some Applications

  • Part of
  • Ge Chen, Changlong Yao, Tiande Guo
  • Journal:
    Advances in Applied Probability / Volume 46 / Issue 2 / June 2014
    Published online by Cambridge University Press:
    22 February 2016, pp. 307-324
    Print publication:
    June 2014
    • Article
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  • In this paper we estimate the expectation of the size of the largest component in a supercritical random geometric graph; the expectation tends to a polynomial on a rate of exponential decay. We sharpen the expectation's asymptotic result using the central limit theorem. Similar results can be obtained for the size of the biggest open cluster, and for the number of open clusters of percolation on a box, and so on.