Stochastic Loewner evolution in multiply connected domains |
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Authors: | Robert O Bauer Roland M Friedrich |
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Institution: | 1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA;2. Institute for Advanced Study, Princeton, NJ 08540, USA |
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Abstract: | We construct radial stochastic Loewner evolution in multiply connected domains, choosing the unit disk with concentric circular slits as a family of standard domains. The natural driving function or input is a diffusion on the associated moduli space. The diffusion stops when it reaches the boundary of the moduli space. We show that for this driving function the family of random growing compacts has a phase transition for and , and that it satisfies locality for . To cite this article: R.O. Bauer, R.M. Friedrich, C. R. Acad. Sci. Paris, Ser. I 339 (2004). |
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