On radial stochastic Loewner evolution in multiply connected domains
| dc.creator | Bauer, Robert O. | |
| dc.creator | Friedrich, Roland M. | |
| dc.date | 2004-12-02 | |
| dc.date | 2005-03-09 | |
| dc.date.accessioned | 2026-07-07T05:14:55Z | |
| dc.date.available | 2026-07-07T05:14:55Z | |
| dc.description | We discuss the extension of radial SLE to multiply connected planar domains. First, we extend Loewner's theory of slit mappings to multiply connected domains by establishing the radial Komatu-Loewner equation, and show that a simple curve from the boundary to the bulk is encoded by a motion on moduli space and a motion on the boundary of the domain. Then, we show that the vector-field describing the motion of the moduli is Lipschitz. We explain why this implies that "consistent," conformally invariant random simple curves are described by multidimensional diffusions, where one component is a motion on the boundary, and the other component is a motion on moduli space. We argue what the exact form of this diffusion is (up to a single real parameter $κ$) in order to model boundaries of percolation clusters. Finally, we show that this moduli diffusion leads to random non-self-crossing curves satisfying the locality property if and only if $κ=6$. | |
| dc.description | Proof of Theorem 6.1 corrected | |
| dc.identifier | https://arxiv.org/abs/math/0412060 | |
| dc.identifier | http://arxiv.org/abs/math/0412060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73466 | |
| dc.subject | Probability | |
| dc.subject | Complex Variables | |
| dc.title | On radial stochastic Loewner evolution in multiply connected domains | |
| dc.type | text |