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

Preprint

Open access

English

Publication date2001

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.

Classification

NoteThis is a copy of an old preprint from 2001, which I will perhaps update in the future

Affiliation

Citation (ISO format)

SMIRNOV, Stanislav. Critical percolation in the plane : I. Conformal invariance and Cardy’s formula. II. Continuum scaling limit. 2001.

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