Stochastic Loewner evolution in doubly connected domains

Details Stochastic Loewner evolution in doubly connected domains Stochastic Loewner evolution in doubly connected domains

2003-10-22

arxiv.org/abs/math/0310350v3

Mathematics

Probability

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

Scientific paper

This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus SLE$_\kappa$ and radial SLE$_\kappa$. 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$_\kappa$ 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$_2$.

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