Explosive percolation via control of the largest cluster

Details Explosive percolation via control of the largest cluster Explosive percolation via control of the largest cluster

2010-05-14

arxiv.org/abs/1005.2504v2

Phys. Rev. Lett. 105, 035701 (2010)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures, final version

Scientific paper

10.1103/PhysRevLett.105.035701

We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of $1.23\pm0.03$, close to that of watersheds.

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