DISTRIBUTIONS OF ABSOLUTE CENTRAL MOMENTS FOR RANDOM-WALK SURFACES

We study periodic Brownian paths, wrapped around the surface of a cyli nder. One characteristic of such a path is its width square, w(2), def ined as its variance. Though the average of w(2) over all possible pat hs is well known, its full distribution function was investigated only recently. Generalizing w(2) to w((N)), defined as the Nth power of th e magnitude of the deviations of the path from its mean, we show that the distribution functions of these also scale and obtain the asymptot ic behaviour for both large and small w((N)).