  We focus on the problem of an impurity-free billiard with a random
position-dependent boundary coupling to the environment. The response functions
of such an open system can be obtained non-perturbatively from a supersymmetric
generating functional. The derivation of this functional is based on averaging
over the escape rates and results in a non-linear ballistic $\sigma $-model,
characterized by system-specific parameters. Particular emphasis is placed on
the {}``whispering gallery modes'' as the origin of surface diffusion modes in
the limit of large dimensionless conductance.
