Abstract. 
We study a dynamical system which models particle propagation in a
one-dimensional, inhomogeneous, anisotropic medium. Simulations have
suggested that, over time, a uniform initial particle density develops an
increasingly irregular fine-structure instead of converging to a limit.
Yet a diffusive coarse-graining yields a Gaussian limit distribution. We
explain these findings analytically.
(Joint work with T. Simula and L. Leskelä)