This award supports cooperative research in the mathematical analysis of interacting particle systems between a group of U.S. scientists headed by Joel Lebowitz of Rutgers University and five Brazilian mathematicians: E.D. Andjel, P.A. Ferrari, J.A. Galves and R.H. Schonmann of the Universidade de Sao Paulo and M.A. Vares of the Instituto de Matematica Pura e Aplicada (IMPA) of CNPq in Rio de Janeiro. The researchers will continue and strengthen a five year long collaboration in the analysis of interacting particle systems and their hydrodynamical limits, an active field of research in mathematics and physics. These latter limits relate interacting particle systems to hydrodynamical partial differential equations and are useful in understanding those equations. This collaboration has been very fruitful, resulting in the publication of at least eleven papers on interacting particle systems. The original motivation for this field arose from stochastic mechanics where the objective was to use probabilistic models in the study of the temporal evolution of systems with classical equilibrium states. Such models appear naturally, for example, as algorithms for making Monte Carlo simulations of Gibbs measures. It soon became clear that the same techniques could also be applied to models from biology, ecology, and the behavioral sciences. Future work by the researchers will center on obtaining more information about interacting systems, including relating microscopic and macroscopic fluctuations, extending previous results to the case where large deviations with unusual scalings are expected, and applying these results to more general settings, for example, particles moving under deterministic dynamics and interacting Brownian motions or random walks.
