Communications in Mathematical Physics

, Volume 114, Issue 4, pp 549–552 | Cite as

On the uniqueness of the infinite cluster in the percolation model

  • A. Gandolfi
  • G. Grimmett
  • L. Russo


We simplify the recent proof by Aizenman, Kesten and Newman of the uniqueness of the infinite open cluster in the percolation model. Our new proof is more suitable for generalization in the direction of percolation-type processes with dependent site variables.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. Gandolfi
    • 1
  • G. Grimmett
    • 2
  • L. Russo
    • 3
  1. 1.Department of Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands
  2. 2.School of MathematicsUniversity of BristolEngland
  3. 3.Department of MathematicsUniversity of Rome IIRomeItaly

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