Stanislav Smirnov
Published 2009-09-24Version 1
We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of the crossing probabilities and Cardy's formula. Then we prove existence, uniqueness, and conformal invariance of the continuum scaling limit.
Comments: This is a copy of an old preprint from 2001, which I will perhaps update in the future
Critical percolation: the expected number of clusters in a rectangle
Relations between invasion percolation and critical percolation in two dimensions
On the chemical distance in critical percolation
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