Critical percolation: The expected number of clusters in a rectangle

Clément Hongler, Stanislav Smirnov

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)735-756
Number of pages22
JournalProbability Theory and Related Fields
Issue number3-4
Publication statusPublished - Dec 2011
Externally publishedYes


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