Duality of chordal SLE, II
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 3, p. 740-759

We improve the geometric properties of processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for κ∈(4, 8), the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed x∈ℝ∖{0} is the image of some trace started from a random point. Using this fact together with a similar proposition in the case that κ≥8, we obtain a description of the boundary of a standard chordal SLE(κ) hull for κ>4, at a finite stopping time. Finally, we prove that for κ>4, in many cases, a chordal or strip trace a.s. ends at a single point.

Nous améliorons des résultats précédemment obtenus concernant les propriétés géométriques des processus , que nous utilisons ensuite pour étudier la propriété dite de dualité des processus SLE. Nous prouvons que pour κ∈(4, 8), la frontière de l'enveloppe d'un SLE(κ) chordal standard arrêté quand il disconnecte un point fixe x∈ℝ\{0} de l'infini est une courbe issue d'un point aléatoire. Nous obtenons ainsi une description de la frontière de l'enveloppe d'un SLE(κ) pour κ>4. Finalement, nous démontrons que pour κ>4, dans de nombreux cas, la courbe de processus généralisés (par exemple dans une bande) se termine presque sûrement en un point unique.

DOI : https://doi.org/10.1214/09-AIHP340
Classification:  30C20,  60H05
Keywords: SLE, duality, coupling technique
@article{AIHPB_2010__46_3_740_0,
     author = {Zhan, Dapeng},
     title = {Duality of chordal SLE, II},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {3},
     year = {2010},
     pages = {740-759},
     doi = {10.1214/09-AIHP340},
     zbl = {1200.60071},
     mrnumber = {2682265},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2010__46_3_740_0}
}
Zhan, Dapeng. Duality of chordal SLE, II. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 3, pp. 740-759. doi : 10.1214/09-AIHP340. http://www.numdam.org/item/AIHPB_2010__46_3_740_0/

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