This is a Taught Course Centre module.

Lectures: Tuesday, 9-11 am (in room B0.06)

First lecture: Tuesday 16th October. Note: extra lecture Friday 19th October 12-14 h.

Content: Large deviations; Gibbs measure (statistical mechanics); mathematics of phase transitions

Lecture 1: Introduction and Cramer's theorem

Lecture 2: Cramer's theorem and Sanov's theorem

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Material (Lecture Notes):

(1) Lecture notes Mathematical Statistical Mechanics, CDIAS Series A, No. 30, 2006 (pdf)

(2) Lecture 'Large deviations for stochastic processes' (pdf)

NOTES:

Chapter 1 (pdf)

Chapter 2.1 (pdf)

Chapter 2.2 (pdf)

Chapter 2.3 (pdf)

Chapter 3.1 (pdf)

Chapter 3.2 (pdf)

Chapter 3.3 (pdf)

Chapter 4 (pdf)

Chapter 5 (pdf)

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References:

[1] A. Dembo & O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed., Springer New York (1998).

[2] F. d. Hollander, Large Deviations, AMS (2000).

[3] E. Olivieri & M.E. Vares, Large Deviations and Metastability, Cambridge University Press (2005).

[4] C.-E. Pfister, Thermodynamical aspects of classical lattice systems. In In and Out of Equilibrium. Probability with a Physics Flavor, ed. V. Sidoravicius. Progress in Probability 51, 393-472, Birkhäuser Basel (2002).

[5] H.O. Georgii, Large Deviations and Maximum Enrtopy Principle For Interacting Random fields on $ \Z^d$ , Annals of Probability Vol. 21, 1845-1875, (1993).