# 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} }

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…

## One Citation

Isoperimetry in supercritical bond percolation in dimensions three and higher

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2018

We study the isoperimetric subgraphs of the infinite cluster $\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with $d\geq 3$. Specifically, we consider the subgraphs of…

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