This is the public webpage of the course “A Medley of Advance Probability”. This page contains only basic information/presentation about this course – more details, links to the videos of the lectures and to the lecture notes – can be found on this other WEBPAGE accessible to the registered students only.
We will review various topics of probability theory, with the goal to provide a short selfcontained introduction to each of them, and try to describe the type of ideas and techniques that are used.
Topics covered will be: Lévy processes (and continuousstate branching processes), large deviation theory, large random matrices.
The
goal is for each of the topics that will be covered to provide:

A general introduction to the subject
 An example of one of
the main statements, and some of the ideas that go into the proof
Martingales, Markov chains, Brownian motion and stochastic calculus.
This course will be delivered online.
Videos of the lectures will be posted on the website each week. At the end of each of the three chapters, an exercise sheet will be posted, and a virtual exercise “class” will be organized in weeks 6, 10 and 14. All this is accessible only to registered students.