Multiplicities of a random sausage (Q1332280)

A particle that executes a transient random walk or a transient Lévy process on some group is considered. Attach a set to the particle and trace out a sausage. Each point in the sausage that has been traced out over the interval \([0,t]\) has an associated multiplicity -- the amount of time in \([0,t]\) that the point has been covered by the moving set. Using potential theory, the author investigates the asymptotics as \(t \to \infty\) of the ensemble of multiplicities. The results involve some interesting connections with the theory of Fredholm integral equations.