Stochastic Loewner evolution in doubly connected domains

Dapeng Zhan

paper

Stochastic Loewner evolution in doubly connected domains

arXiv:math/0310350

Abstract

This paper introduces the annulus SLE $_{κ}$ processes in doubly connected domains. Annulus SLE $_{6}$ has the same law as stopped radial SLE $_{6}$ , up to a time-change. For $κ \neq = 6$ , some weak equivalence relation exists between annulus SLE $_{κ}$ and radial SLE $_{κ}$ . Annulus SLE $_{2}$ is the scaling limit of the corresponding loop-erased conditional random walk, which implies that a certain form of SLE $_{2}$ satisfies the reversibility property. We also consider the disc SLE $_{κ}$ process defined as a limiting case of the annulus SLE's. Disc SLE $_{6}$ has the same law as stopped full plane SLE $_{6}$ , up to a time-change. Disc SLE $_{2}$ is the scaling limit of loop-erased random walk, and is the reversal of radial SLE $_{2}$ .

45 pages, no figures, published in Probability Theory and Related Fields

References in corpus (1)

Critical percolation in annuli and $S L E_{6}$