Percolation critique dans le plan: invariance conforme, formule de Cardy, objets limites

Translated title of the contribution: Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits

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Abstract

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 [7]) and find their values (predicted by Cardy in [4], 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 [10].

Translated title of the contributionCritical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits
Original languageFrench
Pages (from-to)239-244
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume333
Issue number3
DOIs
Publication statusPublished - 1 Aug 2001
Externally publishedYes

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