Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.

@article{Sasidevan2013ContinuumPO,
  title={Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.},
  author={V. Sasidevan},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 2},
  pages={
          022140
        }
}
  • V. Sasidevan
  • Published 1 February 2013
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between R and R+dR is proportional to R(-(a+1)), where a>2. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range… 

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