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arxiv: 0909.4499 · v1 · submitted 2009-09-24 · 🧮 math.PR · math-ph· math.CV· math.MP

Critical percolation in the plane

Stanislav Smirnov This is my paper
classification 🧮 math.PR math-phmath.CVmath.MP
keywords conformalinvariancescalingcriticallimitpercolationcalculatecardy
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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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