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• W3099211817 abstract "Standard stochastic Loewner evolution (SLE) is driven by a continuous Brownian motion, which then produces a continuous fractal trace. If jumps are added to the driving function, the trace branches. We consider a generalized SLE driven by a superposition of a Brownian motion and a stable Lévy process. The situation is defined by the usual SLE parameter, κ, as well as α, which defines the shape of the stable Lévy distribution. The resulting behaviour is characterized by two descriptors: p, the probability that the trace self-intersects, and , the probability that it will approach arbitrarily close to doing so. Using Dynkin's formula, these descriptors are shown to change qualitatively and singularly at critical values of κ and α. It is reasonable to call such changes 'phase transitions'. These transitions occur as κ passes through four (a well-known result) and as α passes through one (a new result). Numerical simulations are then used to explore the associated touching and near-touching events." @default.
• W3099211817 created "2020-11-23" @default.
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• W3099211817 date "2006-01-03" @default.
• W3099211817 modified "2023-09-23" @default.
• W3099211817 title "Stochastic Loewner evolution driven by Lévy processes" @default.
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• W3099211817 doi "https://doi.org/10.1088/1742-5468/2006/01/p01001" @default.
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