Diffusing polygons and SLE($\kappa,\rho$)

Abstract

We give a geometric derivation of SLE($\kappa,\rho$) in terms of conformally invariant random growing subsets of polygons. We relate the parameters $\rho_j$ to the exterior angles of the polygons. We also show that SLE($\kappa,\rho$) can be generated by a metric Brownian motion, where metric and Brownian motion are coupled and the metric ist the pull-back metric of the Euclidean metric of an evolving polygon.