MOMENTS OF INERTIA AND THE SHAPES OF BROWNIAN PATHS

We compute the joint probability law of the principal moments of inert ia of Brownian paths (open or closed), using constrained path integral s and random matrix theory. The case of two-dimensional paths is discu ssed in detail. In particular, we show that the ratio of the average v alues of the largest and smallest moments is equal to 4.99 (open paths ) and 3.07 (closed paths). We also present results of numerical simula tions, which include investigation of the relationships between the mo ments of inertia and the arithmetic area enclosed by a path.