I'm giving a course on large deviations this term. Here is the course schedule. Many large systems, such as communication networks, exhibit failure behaviour which becomes exponentially rare as some parameter of the system varies.
Large deviations is the study of such exponentially decaying probabilities.
It has applications to performance analysis, entropy, simulation methodology and hypothesis testing, among other topics. This course will provide an introduction to large deviations, illustrated and motivated by examples. The theory covered will resemble the following. Large deviations principle. Large deviations for jump Markov processes.