Abstract
This seventh lecture is devoted to an introduction to the theory of large deviations. After recalling the elementary calculation of the large deviation function of a sum of independent random variables, some convexity and analyticity properties of the large deviation function of the density of a fluid and its link with free energy were established. The difference, in terms of the large deviation function, between the case of an instantaneous density profile and that of an empirical density profile obtained by averaging the profile over a long time range has been discussed. The way to calculate the large deviation functions of density or current of an arbitrary Markov process has been explained: most often, this amounts to calculating the largest eigenvalue of a suitably deformed Markov matrix.
