Critical Percolation in the Plane. I. Conformal Invariance and Cardy’s Formula. Ii. Continuum Scaling Limit


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… (More)