Simulation of the wiener sausage

The volume of a region visited by a spherical Brownian particle for a time t, known as the Wiener sausage, is an important random variable characterizing Brownian motion. A Brownian dynamics simulation is used to study statistical properties of the Wiener sausage volume. We show that the probability density is closely approximated by a Gaussian distribution not only at asymptotically long times, but over a wide range of times as well. We also refine the expression for the dispersion by finding a correction term for the long-time asymptotic dependence.