Fractal measures of diffusion in the presence of random fields

We study diffusion in a linear chain where random fields are located at each site and can accept the values ±E with equal probability. While the average density distribution of a random walker scales and is described by a single exponent, it requires an infinite hierarchy of exponents ± to characterize the fluctuations. Their density distribution f(±) is a single-hump function and depends continuously on the magnitude of the field E.