Surface area of the domain visited by a spherical Brownian particle.

A spatial domain swept out by a spherical particle, whose center follows a Wiener trajectory, is referred to as a Wiener sausage. The present study focuses on the surface area of the Wiener sausage. Using intuitive arguments we derive the mean and variance of the surface area, as well as the asymptotic behavior of its probability density in the limits when the area tends to zero and infinity.