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2012 Concentration estimates for the isoperimetric constant of the supercritical percolation cluster
Eviatar Procaccia, Ron Rosenthal
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Electron. Commun. Probab. 17: 1-11 (2012). DOI: 10.1214/ECP.v17-2185

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.

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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

Information

Accepted: 23 July 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1261.60094
MathSciNet: MR2955495
Digital Object Identifier: 10.1214/ECP.v17-2185

Subjects:
Primary: 60K35
Secondary: 82B43

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