Abstract
For a given graph G, let \(\theta _{G}(p) = P_{p}(0 \leftrightarrow \infty )\) (or just θ(p) when G is clear from the context). From the definition of p c we know that θ(p) = 0 for any p < p c , and θ(p) > 0 whenever p > p c . A major and natural question that arises is: Does θ(p c )= 0 or θ(p c ) > 0?.
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- 1.
The reason we need to deal only with these cases is explained in Chap. 4
References
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Benjamini, I. (2013). Critical Percolation on Non-Amenable Groups. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_8
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DOI: https://doi.org/10.1007/978-3-319-02576-6_8
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