# 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 } }

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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