# Large deviations and statistical mechanics

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
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**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)
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**(2) Lecture 'Large deviations for stochastic processes' (pdf)
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**NOTES:
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**References:**

**[1] A. Dembo & O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed., Springer New York (1998).
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**[2] F. d. Hollander, Large Deviations, AMS (2000).
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**[3] E. Olivieri & M.E. Vares, Large Deviations and Metastability, Cambridge University Press (2005).
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**[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).
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**[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).
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