- Lecturer: Prof. Hugo Touchette
- Module information/syllabus

- [HT2011]

H. Touchette, A basic introduction to large deviations: Theory, applications, simulations, in R. Leidl and A. K. Hartmann (eds), Modern Computational Science 11: Lecture Notes from the 3rd International Oldenburg Summer School, BIS-Verlag der Carl von Ossietzky Universitat Oldenburg, 2011. arxiv:1106.4146 | errata at the end of the arxiv version | summer school website - [HT2009]

H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478, 1-69, 2009. arxiv:0804.0327 | published version - [HT2018]

H. Touchette, Introduction to dynamical large deviations of Markov processes, Physica A 504, 5, 2018

arxiv:1705.06492 | published version - [DZ1998]

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Springer, 1998.

Springer | Amazon | Google books - [GS2001]

G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford, 2001.

Amazon

- [J2010]

K. Jacobs, Stochastic Processes for Physicists, Cambridge, 2010.

Amazon

- Week 1: Elements of
probability theory

- Lecture notes
- Notes: Probability (by Oscar Bandtlow at QMUL)
- Reading: Sections not covered in the notes, especially the
section on the Central Limit Theorem

- Exercise sheet

- Week 2: Examples of large
deviations and the large deviation principle

- Lecture notes
- Notes: Sections 2.1 and 2.2 HT2011; sections 2 and 3.1 of HT2009

- Reading: Other examples in notes above and Appendix B of HT2009

- Exercises: HT2011 exercises 2.7.1-2.7.5

- Week 3: Varadhan's
Theorem and the Gärtner-Ellis Theorem

- Lecture notes
- Notes: Sections 2.3 and 2.4 of HT2011; sections 3.3 and 3.5.4
of HT2009

- Reading: Properties of SCGFs and rate functions, sections 3.5 of HT2009
- Further reading: Legendre-Fenchel transforms in a nutshell
- Exercises: HT2011 exercises 2.7.6-2.7.10

- Week 4: IID sample means
and Sanov's Theorem

- Lecture notes
- Notes: Section 3.1 of HT2011; section 4.1 of HT2009

- Reading: Contraction principle, section 2.5 of HT2011 and
section 3.6 of HT2009

- Exercises: HT2011 exercises 3.6.1, 3.6.8, 3.6.9
- Extra exercises: HT2011 exercises 3.6.2-3.6.7

- Week 5: Large deviations
of Markov chains

- Lecture notes
- Notes: Section 3.2 of HT2011; section 4.3 of HT2009

- Reading: Continuous-time processes, section 3.3 of HT2011; GS
Chapter 6

- Exercises: HT2011 exercises 3.6.10 and 3.6.12

- Week 6: Continuous-time
Markov processes

- Lecture notes
- Other notes: Stochastic Models of Complex Systems (by S. Grosskinsky at Warwick University)
- Reading: GS2001 Chapters 8, 9 and 13 and; J2010 Chapters 3 and 8

- Exercises: Problems in GS001, Chapters 8, 9 and 13

- Week 7: Large deviations
of continuous-time processes

- Lecture notes
- H. Touchette, Introduction to dynamical large deviations of Markov processes.
- Reading: Chap. 3 of DZ1998

- Exercises: Problems 3.6.11-3.6.13 in HT2011 (see errata
list at the end for corrections) plus exercises mentioned in lecture
notes

- Week 8: Physical
applications

- Lecture notes
- Reading: HT2009 Sec. 6. S.

- Extra reading: Symmetrization of non-hermitian operators: see
notes on Markov processes
and
diffusions and large
deviation theory of
Markov processes (password protected: ask me for access)

- Exercises: See lecture notes

- Large deviation theory: History, sources, references, and pointers
- Notes: Legendre-Fenchel transforms in a nutshell. pdf
- Video: Large deviations and statistical mechanics
- Video: Large deviations in statistical mechanics. video (wma) | video (flash)

Copyright
©
HT 2013