13-12 Yilun Shang

subcritical inhomogeneous percolation on general graphs (176K, Postscript) Feb 21, 13

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Abstract. We study an inhomogeneous bond percolation process on graphs with general degree sequences. The edges of the host graph $G$ are occupied independently with different probabilities. We show that the percolation phenomenon will not occur if the occupation probabilities are less than $(1-arepsilon)/(\sigma riangle+ ilde{d})$. Here, $\sigma$, $ riangle$ and $ ilde{d}$ are the spectral gap of the normalized Laplacian, maximum degree and second order average degree of the host graph $G$, respectively.

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