Professor Ellis studies the asymptotic behavior of random systems using the theory of large deviations, which focuses on the exponential decay of probabilities in those systems. He has applied the theory to a wide range of problems in which detailed information on rare events is required. These include queueing systems as well as systems arising in statistical mechanics, including spin models and models of coherent structures in turbulence. In recent work he has used the theory of large deviations and the theory of convex functions to understand the equivalence and nonequivalence of the microcanonical, canonical, and generalized canonical ensembles both at the thermodynamic level and at the level of equilibrium macrostates. These ensembles are probability distributions used to describe the behavior of particles in statistical mechanical systems.