Critical percolation in the plane : I. Conformal invariance and Cardy&#039;s formula. II. Continuum scaling limit

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Title		Critical percolation in the plane : I. Conformal invariance and Cardy's formula. II. Continuum scaling limit
Author		Smirnov, Stanislav
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.
Identifiers		arXiv: 0909.4499
Note		This is a copy of an old preprint from 2001, which I will perhaps update in the future
Full text		Preprint (189 Kb) - Free access
Structures		Faculté des sciences / Section de mathématiques
Citation (ISO format)		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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