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Titolo:
Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
Autore:
Smirnov, S;
Indirizzi:
Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden Royal Inst Technol Stockholm Sweden S-10044 h, S-10044 Stockholm, Sweden
Titolo Testata:
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
fascicolo: 3, volume: 333, anno: 2001,
pagine: 239 - 244
SICI:
0764-4442(20010801)333:3<239:CPITPC>2.0.ZU;2-1
Fonte:
ISI
Lingua:
ENG
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
11
Recensione:
Indirizzi per estratti:
Indirizzo: Smirnov, S Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden Royal Inst Technol Stockholm Sweden S-10044 Stockholm, Sweden
Citazione:
S. Smirnov, "Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits", CR AC S I, 333(3), 2001, pp. 239-244

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]. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

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Documento generato il 01/12/20 alle ore 15:46:35