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Probability Theory and Related Fields

, Volume 111, Issue 4, pp 551–564 | Cite as

Exceptional planes of percolation

  • Itai Benjamini
  • Oded Schramm
Article

Abstract.

Consider the standard continuous percolation in ℝ4, and choose the parameters so that the induced percolation on a fixed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.

Mathematics Subject Classification (1991): 82B43 82C43 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Itai Benjamini
    • 1
  • Oded Schramm
    • 1
  1. 1.The Weizmann Institute, Rehovot 76100, Israel e-mail: [itai;schramm]@wisdom.weizmann.ac.ilIL

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