SLE and conformal invariance

Jean Bertoin

Séminaire Bourbaki (2003-2004)

  • Volume: 46, page 15-28
  • ISSN: 0303-1179

Abstract

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The so-called Stochastic Loewner Evolutions form a family of random curves in the complex plane, which enjoy a (statistical) conformal invariance property. They have a crucial role in the analysis of the asymptotic behaviour of many discrete models in statistical physics. In particular, they have yielded rigorous proofs of several important conjectures in this field.

How to cite

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Bertoin, Jean. "SLE et invariance conforme." Séminaire Bourbaki 46 (2003-2004): 15-28. <http://eudml.org/doc/252142>.

@article{Bertoin2003-2004,
abstract = {Les processus de Schramm-Loewner (SLE) induisent des courbes aléatoires du plan complexe, qui vérifient une propriété d’invariance conforme. Ce sont des outils fondamentaux pour la compréhension du comportement asymptotique en régime critique de certains modèles discrets intervenant en physique statistique ; ils ont permis notamment d’établir rigoureusement certaines conjectures importantes dans ce domaine.},
author = {Bertoin, Jean},
journal = {Séminaire Bourbaki},
keywords = {stochastic Loewner equation; conformal invariance; planar brownian motion; percolation; random walk; scaling limit},
language = {fre},
pages = {15-28},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {SLE et invariance conforme},
url = {http://eudml.org/doc/252142},
volume = {46},
year = {2003-2004},
}

TY - JOUR
AU - Bertoin, Jean
TI - SLE et invariance conforme
JO - Séminaire Bourbaki
PY - 2003-2004
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 46
SP - 15
EP - 28
AB - Les processus de Schramm-Loewner (SLE) induisent des courbes aléatoires du plan complexe, qui vérifient une propriété d’invariance conforme. Ce sont des outils fondamentaux pour la compréhension du comportement asymptotique en régime critique de certains modèles discrets intervenant en physique statistique ; ils ont permis notamment d’établir rigoureusement certaines conjectures importantes dans ce domaine.
LA - fre
KW - stochastic Loewner equation; conformal invariance; planar brownian motion; percolation; random walk; scaling limit
UR - http://eudml.org/doc/252142
ER -

References

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