Duality of Schramm-Loewner evolutions

Julien Dubédat

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 5, page 697-724
  • ISSN: 0012-9593

Abstract

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In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal SLE κ , κ > 4 , and appropriate versions of SLE κ ^ , κ ^ = 16 / κ .

How to cite

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Dubédat, Julien. "Duality of Schramm-Loewner evolutions." Annales scientifiques de l'École Normale Supérieure 42.5 (2009): 697-724. <http://eudml.org/doc/272203>.

@article{Dubédat2009,
abstract = {In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal $\mathrm \{SLE\}_\kappa $, $\kappa &gt;4$, and appropriate versions of $\mathrm \{SLE\}_\{\hat\{\kappa \}\}$, $\hat\{\kappa \}=16/\kappa $.},
author = {Dubédat, Julien},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Schramm-Loewner evolution; duality; partition function},
language = {eng},
number = {5},
pages = {697-724},
publisher = {Société mathématique de France},
title = {Duality of Schramm-Loewner evolutions},
url = {http://eudml.org/doc/272203},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Dubédat, Julien
TI - Duality of Schramm-Loewner evolutions
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 5
SP - 697
EP - 724
AB - In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal $\mathrm {SLE}_\kappa $, $\kappa &gt;4$, and appropriate versions of $\mathrm {SLE}_{\hat{\kappa }}$, $\hat{\kappa }=16/\kappa $.
LA - eng
KW - Schramm-Loewner evolution; duality; partition function
UR - http://eudml.org/doc/272203
ER -

References

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  15. [15] W. Werner, Girsanov’s transformation for SLE ( κ , ρ ) processes, intersection exponents and hiding exponents, Ann. Fac. Sci. Toulouse Math.13 (2004), 121–147. Zbl1059.60099MR2060031
  16. [16] W. Werner, Random planar curves and Schramm-Loewner evolutions, in Lectures on probability theory and statistics, Lecture Notes in Math. 1840, Springer, 2004, 107–195. Zbl1057.60078MR2079672
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