2004/08/11 by Robert O. Bauer, Bauer, Robert O., R. Friedrich +2
Mathematics · #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #math.CV #math.PR
paper · pdf · doi:10.48550/arxiv.math/0408157
Corrected version, references added
arxiv created 2004/09/16 · arxiv updated 2009/12/01
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.