Critical Percolation: the Expected Number of Clusters in a Rectangle

We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In par- ticular 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 in principle should provide a new approach to establishing conformal invariance of percolation


Published in:
Probability Theory and Related Fields, 151, 735-756
Year:
2011
Publisher:
Springer Verlag
ISSN:
0178-8051
Laboratories:




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