Brownian forgery of statistical dependences

摘要

The balance held by Brownian motion between temporal regularity andrandomness is embodied in a remarkable way by Levy's forgery of continuousfunctions. Here we describe how this property can be extended to forgearbitrary dependences between two statistical systems, and then establish a newBrownian independence test based on fluctuating random paths. We also arguethat this result allows revisiting the theory of Brownian covariance from aphysical perspective and opens the possibility of engineering nonlinearcorrelation measures from more general functional integrals.