cable bundles, circuit boards, moulded vehicle parts or support beams) whose exact location, shape, and topology may be uncertain. Such problems pose computational challenges for full numerical simulation, particularly in the high frequency regime where the scale of a wavelength is small compared to the size of the structure. The inherent uncertainty that one commonly encounters in the intrinsic geometry may in any case make detailed characterisation of the response irrelevant, even if it was computable.

We therefore take an approach in this paper which uses ray propagation to predict averaged, coarse-grained features of the response, as well as providing statistical information. The averages are not sensitive to structural changes, while providing a platform for the prediction of more detailed statistical characteristics in a post-processing step. The connection between ray propagation and wave-field correlations is based here on transfer or boundary operator approaches [@CHT13]. Transfer operators allow us to present the problem of wave propagation via multiple reflection in a format which mirrors very closely the phase space mappings used for ray propagation (while in principle allowing an exact solution). This transfer operator approach means that we effectively characterise the problem in terms of a Poincaré-section representation, but we emphasise 