MAGNETIC-FIELDS AND BROWNIAN-MOTION ON THE 2-SPHERE

Using constrained path integrals, we study some statistical properties of Brownian paths on the two-dimensional sphere. A generalized Levy law for the probability P(A) that a closed Brownian path encloses an algebraic area A is obtained. Distributions of scaled variables related to the winding of paths around some fixed point are recovered in the asymptotic regime t --> infinity.