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The subject of the course will be an introduction to Large Deviation theory and its applications.
Large deviation theory finds applications in probability theory, statistics, operation research, ergodic theory,
information theory, statistical physics, financial mathematics, etc.
In the second part of the course we will see APPLICATIONS of large deviations to:
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Statistical mechanics and metastability
- Statistics;
- Random walk in random environment
- Polymer chains;
In the choice of applications the teacher will take into account particular interests of the students
that will attend the class.
The course will be self-study course (independent learning under supervision).
It will take place during Semester B Quartile 4. There will be a one-hour lecture where the course content will be presented, followed by one hour self study in class per week. Every Tuesday starting from 24th April from 10.30 until 12.30 at Eurandom yellow room LG 1.110.
During weekly meetings the teacher presents the argument and coaches the students in the learning process.
For the general part and applications you can follow the book by F. Den Hollander and Olivieri Vares.
After taking this course, you will be familiar with
1) Large deviations for I.I.D sequences: in the book of den Hollander the content of Chapter 1 (Cramér's theorem for i.i.d. sequences), Chapter 2 (Sanov's theorem for the empirical measure). You have also the book of Olivieri and Vares Chapter 1 as reference.
2) Large deviations general theory: in the book of den Hollander Chapter 3 (Varadhan's lemma);
3) Large deviations for Markov Sequences: in the book of den Hollander Chapter 4.
You have also the book of Olivieri and Vares Chapter 3.2 as reference.
4) Large deviations for dependent sequences: in the book of den Hollander Chapter 5 (Gärtner-Ellis theorem).
You also have the book of Olivieri and Vares Chapter 3.1 as reference.
Course material
- F.den Hollander, Large deviations, Fields Institute Monograph, Vol.14, American Mathematical Society, Providence RI (2000),
- E. Olivieri, M. E. Vares, Large deviations and metastability. Encyclopedia of Mathematics and its Applications, 100. Cambridge University Press, Cambridge, (2005).
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