Duality of chordal SLE, II

Dapeng Zhan

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 3, page 740-759
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Zhan, Dapeng. "Duality of chordal SLE, II." Annales de l'I.H.P. Probabilités et statistiques 46.3 (2010): 740-759. <http://eudml.org/doc/240299>.

@article{Zhan2010,
abstract = {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&gt;4, at a finite stopping time. Finally, we prove that for κ&gt;4, in many cases, a chordal or strip trace a.s. ends at a single point.},
author = {Zhan, Dapeng},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {SLE; duality; coupling technique},
language = {eng},
number = {3},
pages = {740-759},
publisher = {Gauthier-Villars},
title = {Duality of chordal SLE, II},
url = {http://eudml.org/doc/240299},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Zhan, Dapeng
TI - Duality of chordal SLE, II
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 3
SP - 740
EP - 759
AB - 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&gt;4, at a finite stopping time. Finally, we prove that for κ&gt;4, in many cases, a chordal or strip trace a.s. ends at a single point.
LA - eng
KW - SLE; duality; coupling technique
UR - http://eudml.org/doc/240299
ER -

References

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  6. [6] D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. Springer, Berlin, 1991. Zbl0917.60006MR1083357
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  8. [8] O. Schramm. Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118 (2000) 221–288. Zbl0968.60093MR1776084
  9. [9] D. Zhan. Duality of chordal SLE. Inven. Math. 174 (2008) 309–353. Zbl1158.60047MR2439609
  10. [10] D. Zhan. The scaling limits of planar LERW in finitely connected domains. Ann. Probab. 36 (2008) 467–529. Zbl1153.60057MR2393989
  11. [11] D. Zhan. Reversibility of chordal SLE. Ann. Probab. 36 (2008) 1472–1494. Zbl1157.60051MR2435856

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