[Dualité des évolutions de Schramm-Loewner]
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 , , and appropriate versions of , .
On démontre dans cette note une version de la dualité conjecturée pour les évolutions de Schramm-Loewner, en établissant des identités en distribution exactes entre certains arcs de chordal, , et des versions appropriées de , .
Keywords: Schramm-Loewner evolution, duality, partition function
Mots-clés : Évolution de Schramm-Loewner, dualité, fonction de partition
@article{ASENS_2009_4_42_5_697_0,
author = {Dub\'edat, Julien},
title = {Duality of {Schramm-Loewner} evolutions},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {697--724},
year = {2009},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {Ser. 4, 42},
number = {5},
doi = {10.24033/asens.2107},
zbl = {1205.60147},
language = {en},
url = {https://www.numdam.org/articles/10.24033/asens.2107/}
}
TY - JOUR AU - Dubédat, Julien TI - Duality of Schramm-Loewner evolutions JO - Annales scientifiques de l'École Normale Supérieure PY - 2009 SP - 697 EP - 724 VL - 42 IS - 5 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/asens.2107/ DO - 10.24033/asens.2107 LA - en ID - ASENS_2009_4_42_5_697_0 ER -
%0 Journal Article %A Dubédat, Julien %T Duality of Schramm-Loewner evolutions %J Annales scientifiques de l'École Normale Supérieure %D 2009 %P 697-724 %V 42 %N 5 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/asens.2107/ %R 10.24033/asens.2107 %G en %F ASENS_2009_4_42_5_697_0
Dubédat, Julien. Duality of Schramm-Loewner evolutions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 5, pp. 697-724. doi: 10.24033/asens.2107
[1] , martingales and duality, Ann. Probab. 33 (2005), 223-243. | Zbl | MR
[2] , Euler integrals for commuting SLEs, Journal Statist. Phys. 123 (2006), 1183-1218. | Zbl | MR
[3] , Commutation relations for SLE, Comm. Pure Applied Math. 60 (2007), 1792-1847. | Zbl | MR
[4] , SLE and the free field: Partition functions and couplings, J. Amer. Math. Soc. 22 (2009), 995-1054. | Zbl | MR
[5] & , The configurational measure on mutually avoiding SLE paths, in Universality and renormalization, Fields Inst. Commun. 50, Amer. Math. Soc., 2007, 199-224. | Zbl | MR
[6] , & , Conformal restriction: the chordal case, J. Amer. Math. Soc. 16 (2003), 917-955. | Zbl | MR
[7] , Conformally invariant processes in the plane, Mathematical Surveys and Monographs 114, Amer. Math. Soc., 2005. | Zbl | MR
[8] , & , Conformal invariance of planar loop-erased random walks and uniform spanning trees, Ann. Probab. 32 (2004), 939-995. | Zbl | MR
[9] & , The Brownian loop soup, Probab. Theory Related Fields 128 (2004), 565-588. | Zbl | MR
[10] , Boundary behaviour of conformal maps, Grund. Math. Wiss. 299, Springer, 1992. | Zbl | MR
[11] & , Continuous martingales and Brownian motion, third éd., Grund. Math. Wiss. 293, Springer, 1999. | Zbl | MR
[12] & , Basic properties of SLE, Ann. of Math. 161 (2005), 883-924. | Zbl | MR
[13] & , Contour lines of the two-dimensional discrete Gaussian free field, Acta Math. 202 (2009), 21-137. | Zbl | MR
[14] & , SLE coordinate changes, New York J. Math. 11 (2005), 659-669. | Zbl | MR | EuDML
[15] , Girsanov’s transformation for processes, intersection exponents and hiding exponents, Ann. Fac. Sci. Toulouse Math. 13 (2004), 121-147. | Zbl | MR | Numdam | EuDML
[16] , Random planar curves and Schramm-Loewner evolutions, in Lectures on probability theory and statistics, Lecture Notes in Math. 1840, Springer, 2004, 107-195. | Zbl | MR
[17] , Duality of chordal SLE, Invent. Math. 174 (2008), 309-353. | Zbl | MR
[18] , Reversibility of chordal SLE, Ann. Probab. 36 (2008), 1472-1494. | Zbl | MR
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