Stochastic Loewner evolution in doubly connected domains

By Dapeng Zhan. 2003

69 citations recorded by the source corpus.

Abstract.This paper introduces the annulus SLEκ processes in doubly connected domains. Annulus SLE6 has the same law as stopped radial SLE6, up to a time-change. For κ ≠ 6, some weak equivalence relation exists between annulus SLEκ and radial SLEκ. Annulus SLE2 is the scaling limit of the corresponding loop-erased conditional random walk, which implies that a certain form of SLE2 satisfies the reversibility property. We also consider the disc SLEκ process defined as a limiting case of the annulus SLE’s. Disc SLE6 has the same law as stopped full plane SLE6, up to a time-change. Disc SLE2 is the scaling limit of loop-erased random walk, and is the reversal of radial SLE2.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f0cd13e957de1ddce45724545687af27e7ac181

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Gregory F. Lawler
2. Michel Bauer
3. D. Bernard

In Mathematical Physics

1. D. Bernard
2. Michel Bauer
3. Dapeng Zhan
4. Gregory F. Lawler
5. Julien Dubédat
6. Stanislav Smirnov
7. Wendelin Werner
8. Scott Sheffield

Citations in the corpus

• Reversibility of chordal SLE (2008, background): “It may also be used to study the reversal of the trace of other variations of SLE, for example, SLE(κ,ρ) [5], continuous LERW [14] and annulus SLE [15, 16].”
• 2D growth processes: SLE and Loewner chains (2006, background): “had to be expected because Schramm’s argument implies that conformally invariant curves have to be described by the standard SLEs. SLEs indifferent topologiesthanthatofadisc have been considered: refs.[44,141,10] discussed SLEs in annuli and ref.[14,15,16] defined SLEs in multiply connected domains. T”
• The scaling limits of planar LERW in finitely connected domains. (2006, background): “The reader may see Section 5 in [20] for the detailed proof of a similar proposition.”
• Schramm-Loewner Evolution (2007, background): “[81] D. Zhan (2004), Stochastic Loewner evolution in doubly connected domains.”