Critical percolation in the plane

Details Critical percolation in the plane Critical percolation in the plane

2009-09-24

arxiv.org/abs/0909.4499v1

Mathematics

Probability

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

Scientific paper

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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