Duality of chordal SLE, II
Zhan, Dapeng
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010), p. 740-759 / Harvested from Numdam
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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.

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.

Publié le : 2010-01-01
DOI : https://doi.org/10.1214/09-AIHP340
Classification:  30C20,  60H05 
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     author = {Zhan, Dapeng},
     title = {Duality of chordal SLE, II},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {46},
     year = {2010},
     pages = {740-759},
     doi = {10.1214/09-AIHP340},
     mrnumber = {2682265},
     zbl = {1200.60071},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2010__46_3_740_0}
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Zhan, Dapeng. Duality of chordal SLE, II. Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) pp. 740-759. doi : 10.1214/09-AIHP340. http://gdmltest.u-ga.fr/item/AIHPB_2010__46_3_740_0/

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