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Concentration estimates for the isoperimetric constant of the supercritical percolation cluster

   
@article{ECP2185,
	author = {Eviatar Procaccia and Ron Rosenthal},
	title = {Concentration estimates for the isoperimetric constant of the supercritical percolation cluster},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {Isoperimetric constant ; Percolation, concentration},
	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.},
	pages = {no. 30, 1-11},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-2185},    
        url = {http://ecp.ejpecp.org/article/view/2185}}