  The balance held by Brownian motion between temporal regularity and
randomness is embodied in a remarkable way by Levy's forgery of continuous
functions. Here we describe how this property can be extended to forge
arbitrary dependences between two statistical systems, and then establish a new
Brownian independence test based on fluctuating random paths. We also argue
that this result allows revisiting the theory of Brownian covariance from a
physical perspective and opens the possibility of engineering nonlinear
correlation measures from more general functional integrals.
