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Critical percolation in the plane : I. Conformal invariance and Cardy's formula. II. Continuum scaling limit

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Year 2001
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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arXiv: 0909.4499
Note This is a copy of an old preprint from 2001, which I will perhaps update in the future
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SMIRNOV, Stanislav. Critical percolation in the plane : I. Conformal invariance and Cardy's formula. II. Continuum scaling limit. 2001. https://archive-ouverte.unige.ch/unige:24405

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Deposited on : 2012-12-11

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