Hugo Touchette: Large deviation theory and its applications in statistical physics
The theory of large deviations, initiated by Cramer in the
1930s and later developed by Donsker and Varadhan in the 1970s, is
concerned with the exponential decay of probabilities of fluctuations
in random systems. These probabilities are important in many fields of
study, including statistics, finance, and engineering, as they yield
valuable information about the large fluctuations of many random
systems around their most probable state or trajectory.
From the point of view of statistical physics, the theory of large
deviations can be seen as a generalization of Einstein's theory of
fluctuations. This presentation will explore this and other connections
between large deviation theory and statistical physics in order to show
that large deviation theory is the 'mathematics' of statistical
physics, in the same way that differential geometry, say, is the
mathematics of general relativity.
The presentation will be divided into three one-hour parts covering the following topics:
1. Introduction to large deviation theory
2. Applications for equilibrium systems
3. Applications for nonequilibrium systems
More information about the content of the presentation can be found in the following review paper:
H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478, 1-69, 2009.
http://dx.doi.org/10.1016/j.physrep.2009.05.002
http://arxiv.org/abs/0804.0327