Stochastic Loewner evolution in multiply connected domains

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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 Teichmüller space. The diffusion stops when it reaches the boundary of the Teichmüller space. We show that for this driving function the family of random growing compacts has a phase transition for $κ=4$ and $κ=8$, and that it satisfies locality for $κ=6$.
Corrected version, references added

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Probability, Complex Variables

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http://salesiana.dossiersoluciones.com/handle/123456789/72167

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0408157
 http://arxiv.org/abs/math/0408157

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arXiv