Critical Percolation on Non-Amenable Groups

  • Itai Benjamini
Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 2100)

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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References

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Itai Benjamini
    • 1
  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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