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arXiv · 0909.4499

Critical percolation in the plane

Stanislav Smirnov
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Abstract

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.

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Stanislav Smirnov. 2009-09-24. Critical percolation in the plane. https://arxiv.org/abs/0909.4499

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