An introduction to large deviations
SS 2025
Lectures: Friday 14:15 - 15:45 (+2 UTC), online
Zoom link: Meeting ID: 652 9640 2127, Passcode: 71776632 or click here
Everyone is welcome to participate
Course Description
The large deviations theory is one of the key techniques of modern probability. It concerns with the study of probabilities of rare events and its estimates is the crucial tool required to handle many questions in statistical mechanics, engineering, applied probability, statistics etc. During the course we discuss the following topics:
- Cramer's theorem;
- Notion of large deviation principle;
- Contraction principle;
- Schilder's theorem (LDP for Brownian motion);
- Friedlin-Wentzell theory (LDP for SDE);
- Gärtner-Ellis's theorem;
- Sanov's Theorem;
- Varadhan's lemma;
- Exponential tightness and weak LDP;
- Application of LDP.
The courseis build as the first look at the theory and is oriented on master and PhD students.
Literature
Announcement
PDF File
Lecture Notes
Notes
Course Journal
- April 11 - Introduction and some examples
- April 18 - Cremer's theorem
- April 25 - Proof of Cremer's theorem, definition of large deviations
- May 2 - LDP for empirical means
- May 9 - Lower semi-continuity and goodness of rate functions
- May 16 - Weak LDP and exponential tightness
- May 23 - Schilder's theorem (Part I)
- June 13 - Schilder's theorem (Part II)
- June 20 - Contraction principle and Freidlin-Wentzell theory
- June 27 - Sanov's theorem
- July 4 - Varadhan's lemma
- July 11 - Exponential equivalence
- July 18 - Curie-Weiss model of ferromagnetism (last lecture)
Homework