Abstract
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.
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Hongler, C., Smirnov, S. Critical percolation: the expected number of clusters in a rectangle. Probab. Theory Relat. Fields 151, 735–756 (2011). https://doi.org/10.1007/s00440-010-0313-8
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DOI: https://doi.org/10.1007/s00440-010-0313-8