  We consider the numerical solution of time-harmonic acoustic scattering by
obstacles with uncertain geometries for Dirichlet, Neumann, impedance and
transmission boundary conditions. In particular, we aim to quantify diffracted
fields originated by small stochastic perturbations of a given relatively
smooth nominal shape. Using first-order shape Taylor expansions, we derive
tensor deterministic first kind boundary integral equations for the statistical
moments of the scattering problems considered. These are then approximated by
sparse tensor Galerkin discretizations via the combination technique (Griebel
et al.). We supply extensive numerical experiments confirming the predicted
error convergence rates with poly-logarithmic growth in the number of degrees
of freedom and accuracy in approximation of the moments. Moreover, we discuss
implementation details such as preconditioning to finally point out further
research avenues.
