2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75397We give a geometric derivation of SLE($κ,ρ$) in terms of conformally invariant random growing subsets of polygons. We relate the parameters $ρ_j$ to the exterior angles of the polygons. We also show that SLE($κ,ρ$) 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.ProbabilityComplex Variables60K35text