Reversibility of whole-plane SLE

Reversibility of whole-plane SLE

The main result of this paper is that, for κ ∈ ( 0 , 4 ] , whole-plane SLE κ satisfies reversibility, which means that the time-reversal of a whole-plane SLE κ trace is still a whole-plane SLE κ trace. In addition, we find that the time-reversal of a radial SLE κ trace for κ ∈ ( 0 , 4 ] is a disc SL...

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Veröffentlicht in:Probability theory and related fields 2015-04, Vol.161 (3-4), p.561-618
1. Verfasser: Zhan, Dapeng
Format: Artikel
Sprache:eng
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Zusammenfassung:The main result of this paper is that, for κ ∈ ( 0 , 4 ] , whole-plane SLE κ satisfies reversibility, which means that the time-reversal of a whole-plane SLE κ trace is still a whole-plane SLE κ trace. In addition, we find that the time-reversal of a radial SLE κ trace for κ ∈ ( 0 , 4 ] is a disc SLE κ trace with a marked boundary point. The main tool used in this paper is a stochastic coupling technique, which is used to couple two whole-plane SLE κ traces so that they overlap. Another tool used is the Feynman–Kac formula, which is used to solve a PDE. The solution of this PDE is then used to construct the above coupling.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-014-0554-z