An introduction to large deviation theory and some of its applications in statistical physics

by Hugo Touchette (School of Mathematical Sciences Queen Mary University of London London, UK)

Tuesday 10 Jul 2012, 11:00 → 13:00 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio. G. Marconi)

The aim of these lectures will be to introduce some elements of the mathematical theory of large deviations, as initiated by Cramer in the 1930s and later developed by Donsker and Varadhan in the 1970s, and some applications of these elements in statistical physics. The lectures will start with two sessions covering the following subjects: - Basic results of large deviation theory - Applications in equilibrium statistical physics Then, depending on the interest of the audience, more sessions can be organized on more specialized topics, such as - Applications for stationary nonequilibrium systems - Freidlin-Wentzell theory of noise-perturbed dynamical systems - Donsker-Varadhan theory of large deviations in Markov processes - Nonconvex rate functions and nonconcave entropies - Large deviation simulations The underlying theme of the lectures - and quite an ambitious one at that - is that large deviation theory is the mathematics of statistical physics, in the same way that differential geometry, say, is the mathematics of general relativity or that linear algebra is the mathematics of quantum mechanics. Many examples will be given to illustrate this point.