Abstract
The sixth lecture was devoted entirely to the functions of large deviations associated with empirical measurements of density or current. Starting once again with the example of the Langevin equation in the low-noise limit, it was shown that under certain conditions (such as convexity of the square of the force) the optimal profile associated with an empirical measurement is independent of time. Examples were presented where these conditions are not satisfied, as in the case of a double potential well, giving rise to instanton calculations. These ideas were then applied, again using macroscopic fluctuation theory, to obtain the large current deviation functions of diffusive systems.
