Intrinsic isoperimetry of the giant component of supercritical bond percolation in dimension two

@article{Gold2016IntrinsicIO,
  title={Intrinsic isoperimetry of the giant component of supercritical bond percolation in dimension two},
  author={Julian Gold},
  journal={arXiv: Probability},
  year={2016}
}
  • Julian Gold
  • Published 1 November 2016
  • Mathematics
  • arXiv: Probability
We study the isoperimetric subgraphs of the giant component $\textbf{C}_n$ of supercritical bond percolation on the square lattice. These are subgraphs of $\textbf{C}_n$ having minimal edge boundary to volume ratio. In contrast to the work of Biskup, Louidor, Procaccia and Rosenthal, the edge boundary is taken only within $\textbf{C}_n$ instead of the full infinite cluster. The isoperimetric subgraphs are shown to converge almost surely, after rescaling, to the collection of optimizers of a… 

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  • Julian Gold
  • Mathematics
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