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English

Critical percolation: the expected number of clusters in a rectangle

Publication date2010
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.

Citation (ISO format)
HONGLER, Clement, SMIRNOV, Stanislav. Critical percolation: the expected number of clusters in a rectangle. In: Probability theory and related fields, 2010, p. 27 p. doi: 10.1007/s00440-010-0313-8
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Article (Published version)
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ISSN of the journal0178-8051
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