Large Deviations

Large deviation theory is a part of probability theory that deals with the description of "unlikely" events and determines how fast their probabilities decay.
This turns out to be crucial to study the integrals of exponential functionals of sums of random variables, which come up in many different contexts. Large deviation theory finds applications in ergodic theory, information theory
and statistical physics.
The course will treat large deviations for i.i.d. sequences and and large deviations for empirical measures. General theory and concrete applications will be discussed.

At the end of the module, students are familiar with with the theory of large deviations and are able to apply basic techniques as exponential inequalities.

MA2409 Probability Theory

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

Blackboard, exercise sheet

Amir Dembo, Ofer Zeitouni: Large Deviation Techniques and Applications.
Frank den Hollander: Large Deviations.
Wolfgang König: Große Abweichungen, Techniken und Anwendungen, available here:
http://www.wias-berlin.de/people/koenig/www/Skripte.html

The module examination is based on a written exam (60 minutes) or an oral exam (30 minutes). Students have to reflect the theory of large deviations and are able to adequately apply basic techniques.