  We consider time-harmonic electromagnetic scattering problems on perfectly
conducting scatterers with uncertain shape. Thus, the scattered field will also
be uncertain. Based on the knowledge of the two-point correlation of the domain
boundary variations around a reference domain, we derive a perturbation
analysis for the mean of the scattered field. Therefore, we compute the second
shape derivative of the scattering problem for a single perturbation. Taking
the mean, this leads to an at least third order accurate approximation with
respect to the perturbation amplitude of the domain variations. To compute the
required second order correction term, a tensor product equation on the domain
boundary has to be solved. We discuss its discretization and efficient solution
using boundary integral equations. Numerical experiments in three dimensions
are presented.
