Abstract
We give a geometric derivation of $\text{SLE}(\kappa,\rho)$ in terms of conformally invariant random growing compact subsets of polygons. The parameters $\rho_j$ are related to the exterior angles of the polygons. We also show that $\text{SLE}(\kappa,\rho)$ can be generated by a metric Brownian motion, where metric and Brownian motion are coupled and the metric is a pull-back metric of the Euclidean metric of an evolving polygon.
Citation
Robert O. Bauer. Roland M. Friedrich. "Diffusing polygons and SLE(κ,ρ)." Illinois J. Math. 50 (1-4) 93 - 105, 2006. https://doi.org/10.1215/ijm/1258059471
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