On the Scaling Limits of Planar Percolation

  • Oded Schramm*
  • Stanislav Smirnov†
  • Christophe Garban
Open Access
Part of the Selected Works in Probability and Statistics book series (SWPS)


We prove Tsirelson’s conjecture that any scaling limit of the critical planar percolation is a black noise. Our theorems apply to a number of percolation models, including site percolation on the triangular grid and any subsequential scaling limit of bond percolation on the square grid. We also suggest a natural construction for the scaling limit of planar percolation, and more generally of any discrete planar model describing connectivity properties.

Keywords and phrases

percolation noise scaling limit 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Oded Schramm*
    • 1
  • Stanislav Smirnov†
    • 2
  • Christophe Garban
    • 3
  1. 1.Microsoft Research
  2. 2.Section De Mathématiques, Université De GenèveGenève 4Switzerland
  3. 3.CNRS, ENS LyonLyonFrance

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