Probability Theory and Related Fields

, Volume 151, Issue 3–4, pp 735–756 | Cite as

Critical percolation: the expected number of clusters in a rectangle

  • Clément Hongler
  • Stanislav Smirnov


We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs of points converges to an explicit conformal invariant. Our proof is independent of earlier results and SLE techniques, and might provide a new approach to establishing conformal invariance of percolation.

Mathematics Subject Classification (2000)

Primary 60K35 Secondary 30C35 81T40 82B43 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Section de MathématiquesUniversité de GenèveGeneva 4Switzerland

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