Georgia Institute of Technology College of Sciences

In this talk, we will introduce the classical Cramer's Theorem. The pattern of proof is one of the two most powerful tools in the theory of large deviations. Namely, the upper bound comes from optimizing over a family of Chebychef inequalities; while the lower bound comes from introducing a Radon-Dikodym factor in order to make what was originally "deviant" behavior look like typical behavior. If time permits, we will extend the Cramer's Theorem to a more general setting and discuss the Sanov Theorem. This talk is based on Deuschel and Stroock's .