Uniqueness of the Infinite Percolation Cluster

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


Since we know that for p > p c there is an infinite percolation cluster a.s., it is natural to ask whether it is unique or not. As it turns out the answer to this question leads to a rather rich landscape with applications in group theory and many still open problems. In this section we study the question of the number of infinite clusters in percolation configurations in the regime p > p c .


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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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