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Löwner evolution driven by a stochastic boundary point

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of Bergen, P. O. Box 7803, 5020, Bergen, Norway

    Georgy Ivanov & Alexander Vasil’ev

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  1. Georgy Ivanov
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  2. Alexander Vasil’ev
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Correspondence to Georgy Ivanov.

Additional information

The authors have been supported by the grant of the Norwegian Research Council #204726/V30, by the Nord Forsk network ‘Analysis and Applications’, grant #080151, by the European Science Foundation Research Networking Programme HCAA, and by Meltzerfondet (University of Bergen). This work was completed while the authors were visiting Mittag-Leffler institute, Sweden in the Fall 2011.

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Ivanov, G., Vasil’ev, A. Löwner evolution driven by a stochastic boundary point. Anal.Math.Phys. 1, 387–412 (2011). https://doi.org/10.1007/s13324-011-0019-9

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  • DOI: https://doi.org/10.1007/s13324-011-0019-9

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