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International audienceIf C<sub>1</sub> 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<sub>1</sub> 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

The Mean Perimeter of Some Random Plane Convex Sets Generated by a Brownian Motion