I gave a 4h PhD webinar course covering probabilities, large deviations, spectral methods and thermodynamics of stochastic systems for the online school on Complex Systems and Spectral Methods, organized by m friend Francesco Caravelli. This is a first experiment of an online school, and I really wish that it will be replied. You can find the complete videos here. Unfortunately I didn’t have time to go through the lectures of the other speakers yet, but I’m looking forward to it.
In the meantime, here my own lectures:
Lecture notes can be downloaded here (it’s just a draft, please don’t spread around. And please if you find mistakes report them to me!).