Abstract
We consider the Cheeger constant $\phi(n)$ of the giant component of supercritical bond percolation on $\mathbb{Z}^d/n\mathbb{Z}^d$. We show that the variance of $\phi(n)$ is bounded by $\frac{\xi}{n^d}$, where $\xi$ is a positive constant that depends only on the dimension $d$ and the percolation parameter.
Citation
Eviatar Procaccia. Ron Rosenthal. "Concentration estimates for the isoperimetric constant of the supercritical percolation cluster." Electron. Commun. Probab. 17 1 - 11, 2012. https://doi.org/10.1214/ECP.v17-2185
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