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Critical percolation: the expected number of clusters in a rectangle

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Published in Probability Theory and Related Fields. 2010, p. 27 p.
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.
Stable URL http://archive-ouverte.unige.ch/unige:11886
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Deposited on : 2010-09-24

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