In this Note we study critical site percolation on triangular lattice. We introduce harmonic conformal invariants as scaling limits of certain probabilities and calculate their values. As a corollary we obtain conformal invariance of the crossing probabilities (conjecture attributed to Aizenman by Langlands, Pouliot, and Saint-Aubin in ) and find their values (predicted by Cardy in , we discuss simpler representation found by Carleson). Then we discuss existence, uniqueness, and conformal invariance of the continuum scaling limit. The detailed proofs appear in .
|Translated title of the contribution||Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|Publication status||Published - 1 Aug 2001|