Some active volcanoes on Io are associated with bright annular deposits. Here we characterize the dimensions of the annulus observed at Prometheus. Assuming that relative brightness in images is directly related to areal particle concentration on the surface, we develop a model describing emplacement of particles whose motion is controlled by stochastic processes near the vent and ballistic transport beyond. Stochastic processes are expressed as probability distributions for the important transport variables. By varying the distribution parameters, high particle concentration annuli on the surface come and go. For isotropic ejection from the stochastic region with a fixed energy, subsequent ballistic transport to the surface produces singularities in the areal concentration at r=0 and r=rmax. This areal concentration of particles features peaks corresponding to the singularities. Truncation of the ejection cone such that particles with a single energy are ejected isotopically between 0 and some maximum angle &thgr;0 increases the relative importance of the peak near rmax. Extrapolating the model with a narrow Gaussian energy distribution introduces enough dispersion in the areal concentrations to produce broad annuli. Varying combinations of the truncation angle and relative standard deviation for the energy distribution changes the shape and magnitude of the surface deposit. A truncation angle of 75¿ and a relative standard deviation of 0.08 produce a symmetric annulus closest in shape and size to that observed at Prometheus. From examination of the energetics associated with thermalized particles, we find that many molecular compositions are admissible as annulus constituents at Prometheus.