Critical percolation in the plane

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.

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

Cited by in corpus (2)

• The Length of an SLE - Monte Carlo Studies
• Critical percolation: the expected number of clusters in a rectangle