  Recently discrete dynamical models of walking droplet dynamics have allowed
for fast numerical simulations of their horizontal chaotic motion and
consequently the long-time statistical distribution of the droplet position. We
develop a discrete model for walkers on an elliptical corral with two dominant
eigenmodes. These eigenmodes are excited periodically with each having random,
but correlated, weights. At each iteration the model computes the horizontal
propulsion of the droplet due to impacts with the fluid bath. The propulsion is
calculated based on the interaction of the droplet with the wavefield produced
by the eigenmode excitations. We record the long-time statistics, and
incredibly for such a simple model, they are qualitatively similar to that of
experiments.
