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We establish an exact formula for the average number of edges appearing onthe boundary of the global convex hull of n independent Brownian paths in theplane. This requires the introduction of a counting criterion which amounts to"cutting off" edges that are, in a specific sense, small. The main argumentconsists in a mapping between planar Brownian convex hulls and configurationsof constrained, independent linear Brownian motions. This new formula isconfirmed by retrieving an existing exact result on the average perimeter ofthe boundary of Brownian convex hulls in the plane.

Convex hull of n planar Brownian paths: an exact formula for the average number of edges