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Diffusing polygons and SLE($κ,ρ$)

Robert O. Bauer·Roland M. Friedrich
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Abstract

We 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.

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Robert O. Bauer, Roland M. Friedrich. 2005-06-03. Diffusing polygons and SLE($κ,ρ$). https://arxiv.org/abs/math/0506062

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