Group-invariant Percolation on Graphs

  title={Group-invariant Percolation on Graphs},
  author={Itai Benjamini and Russell Lyons and Yuval Peres and Oded Schramm},
  journal={Geometric \& Functional Analysis GAFA},
Abstract. Let G be a closed group of automorphisms of a graph X. We relate geometric properties of G and X, such as amenability and unimodularity, to properties of G-invariant percolation processes on X, such as the number of infinite components, the expected degree, and the topology of the components. Our fundamental tool is a new masstransport technique that has been occasionally used elsewhere and is developed further here.¶ Perhaps surprisingly, these investigations of group-invariant… 

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