# 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…
1 Citations

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