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Large Deviations

Module MA5417

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
SS 2012WS 2011/2

Basic Information

MA5417 is a semester module in German or English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions

Content

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.

Learning Outcome

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.

Preconditions

MA2409 Probability Theory

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

TypeSWSTitleLecturer(s)Dates
VO 2 Large Deviations Berger Steiger, N. Thu, 14:15–15:45, BC1 BC1 2.02.01
Wed, 08:15–09:45, BC2 BC2 3.5.06
UE 1 Large Deviations (Exercise Session) Berger Steiger, N. Höfelsauer, T. Wed, 12:00–14:00, BC2 BC2 3.5.06

Learning and Teaching Methods

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.

Media

Blackboard, exercise sheet

Literature

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

Module Exam

Description of exams and course work

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.

Exam Repetition

The exam may be repeated at the end of the semester.

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