Large Deviations

Lecture:
Dates:

The lecture has already taken place.

Instructor: Prof. Dr. Nina Gantert
Prerequisites: Probability Theory
A link to the lecture notes of Prof. Gantert's lecture is available here.
Content:

Large deviation theory is a part of probability theory which 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 Markov chains, large deviations for empirical measures and for sample paths and the Gibbs conditioning principle.

Literature:

Amir Dembo, Ofer Zeitouni: Large Deviations Techniques and Applications,
Springer (1998).

Frank den Hollander: Large Deviations,
Fields Institute Monographs (2002).

Final exam:
Assessment regime: oral exams
Exercise classes:
Dates of classes: The exercise classes have already taken place.
Organization of classes: Christian Bartsch 
Exercise sheets (in German):
Sheet 1 Sheet 2 Sheet 3 Sheet 4 Sheet 5 Sheet 6 Sheet 7

 

If you have any questions concerning the exercise classes, please contact Christian Bartsch.