On the Scaling Limits of Planar Percolation

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

Abstract

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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