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The Wiener measure induces a measure of closed, convex, (d-1)-dimensional,Euclidean (hyper-)surfaces that are the convex hulls of closed d-dimensionalBrownian bridges. I present arguments and numerical evidence that this measure,for odd d, is generated by a local classical action of length dimension twothat depends on geometric invariants of the (d-1)-dimensional surface only.

Local Measure of Convex Surfaces induced by the Wiener Measure of Paths