ALGEBRAIC AREAS ENCLOSED BY BROWNIAN CURVES ON BOUNDED DOMAINS

Using constrained path integrals and perturbation theory, we study the algebraic area, A, enclosed by closed Brownian curves on various domains such as rectangles or strips. In the limit of infinitely long curves, the probability distribution P(A) is shown to be Gaussian. The standard deviation [A2]1/2 is simply expressed in terms of the length scales of the problem.