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

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

2011-10-27

arxiv.org/abs/1110.6006v2

Mathematics

Probability

11 Pages, 1 figure

Scientific paper

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.

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