Concentration estimates for the isoperimetric constant of the super critical percolation cluster

Abstract

We consider the Cheeger constant $\varphi (n)$ of the giant component of supercritical bond percolation on ${\mathbb{Z}}^d/n{\mathbb{Z}}^d$. We show that the variance of $\varphi (n)$ is bounded by $\frac{\xi }{n^d}$, where $\xi$ is a positive constant that depends only on the dimension $d$ and the percolation parameter.

11 Pages, 1 figure

References in corpus (2)

• Anomalous heat-kernel decay for random walk among bounded random conductances
• On the range of a random walk in a torus and random interlacements

Cited by in corpus (4)

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• On the range of a random walk in a torus and random interlacements
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