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Percolation on Expanders

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Coarse Geometry and Randomness

Part of the book series: Lecture Notes in Mathematics ((LNMECOLE,volume 2100))

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Abstract

This section is devoted to percolation on finite graphs. More precisely we will try to understand percolation on a sequence of finite graphs, whose number of vertices tends to infinity. Detailed proofs of the material appearing in this section and additional extensions can be found at [ABS04].

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References

  1. N. Alon, I. Benjamini, A. Stacey, Percolation on finite graphs and isoperimetric inequalities. Ann. Probab. 32(3A), 1727–1745 (2004)

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  4. G. Grimmett, Percolation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 321, 2nd edn. (Springer, Berlin, 1999)

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  5. S. Hoory, N. Linial, A. Wigderson, Expander graphs and their applications. Bull. Am. Math. Soc. (N.S.) 43(4), 439–561 (2006) (electronic)

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Benjamini, I. (2013). Percolation on Expanders. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_11

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