If C 1 is the convex hull of the curve of a standard Brownian motion in the complex plane watched from 0 to 1, we consider the convex hulls of C 1 and several rotations of it and compute the mean of the length of their perimeter by elementary calculations. This can be seen geometrically as a study of the exit time by a Brownian motion from certain polytopes having the unit circle as an inscribed one.
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