SLE and alpha-SLE driven by Levy processes

Journal article

Stochastic Loewner evolutions (SLE) with a multiple √κB of Brownian motion B as driving process are random planar curves (if κ ≤ 4) or growing compact sets generated by a curve (if κ > 4). We consider here more general Lévy processes as driving processes and obtain evolutions expected to look like random trees or compact sets generated by trees, respectively. We show that when the driving force is of the form √κB + θ1/αS for a symmetric α-stable Lévy process S, the cluster has zero or posi...

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Authors: Guan, Q; Winkel, M

• Publication status: Published
• Journal: ANNALS OF PROBABILITY
• Volume: 36
• Issue: 4
• Pages: 1221-1266
• Publication date: 2008-07-01
• DOI: 10.1214/07-AOP355
• ISSN: 0091-1798
• Language: English
• Keywords: stochastic Loewner evolution; self-similarity; hitting times; alpha-stable process; Levy process