Large Time Volume of the Pinned Wiener Sausage

We calculate the form of the large time asymptotic expansion of the expected volume of the pinned Wiener sausage associated to a compact set K in Rd in dimensions d⩾3. In each case the leading coefficient is given by the Newtonian capacity of K. If K is a ball of radius a>0 the first three coefficients are calculated explicitly. As a byproduct of our results we obtain the low energy behaviour of the Krein spectral shift function for obstacle scattering systems.