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Critical percolation in the plane: Conformal invariance, Cardy’s formula, scaling limits. (English. Abridged French version) Zbl 0985.60090
Summary: 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 R. Langlands, Ph. Pouliot and Y. Saint-Aubin, Bull. Am. Math. Soc., New Ser. 30, No. 1, 1-61 (1994; Zbl 0794.60109)] and find their values [predicted by J. Cardy, J. Phys. A, Math. Gen. 25, L201–L206 (1992), 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 [the author, “Critical percolation in the plane”, http://www.math.kth.se/~stas/papers].

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B27 Critical phenomena in equilibrium statistical mechanics
82B43 Percolation
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