We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drive the evolution of the galactic density profile. In a dark matter halo, the repeated stochastic perturbations preferentially ring the lowest-order modes with only a very weak dependence on the details of their source. The subsequent redistribution of halo mass is determined only by the mechanics of these modes. The halo profile then evolves toward a universal asymptotic form for a wide variety of noise sources. Such a convergence may help explain the similarity of normal galaxy morphology in diverse environments. A variety of other applications are discussed.