Entropy, Large Deviations, and Scaling Limits

We often model the evolution of a complex system at the lowest or micro level because that is what makes the most physical sense. But if the system is large, we invariably want answers to questions posed on the larger macro or global scale. This then involves the study of equations with a large number of variables and extracting useful information from their solutions. The macroscopic quantities of interest may not contain complete information about the microscopic variables that drive their evolution. Something has to be done to obtain a closed system of equations for quantities of interest. Different contexts require different approaches. We are concerned here with the evolution of large systems of interacting particles or field variables that have some built-in noise and outline some of the work done at the Institute during the last 25 years.