Löwner evolution driven by a stochastic boundary point

We consider evolution in the unit disk in which the sample paths are represented by the trajectories of points evolving randomly under the generalized Loewner equation. The driving mechanism differs from the SLE evolution, but nevertheless solutions possess similar invariance properties.

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Bibliographic Details
Published inAnalysis and mathematical physics Vol. 1; no. 4; pp. 387 - 412
Main Authors Ivanov, Georgy, Vasil’ev, Alexander
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.12.2011
Subjects
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Brownian motion
Shape
Primary 60K35
Löwner equation
Diffusion
Attractor
30C35
Secondary 60J65
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Summary:We consider evolution in the unit disk in which the sample paths are represented by the trajectories of points evolving randomly under the generalized Loewner equation. The driving mechanism differs from the SLE evolution, but nevertheless solutions possess similar invariance properties.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-011-0019-9