Free probability was introduced by D. Voiculescu in the nineties as a probability theory for non-commutative variables endowed with a notion of freeness very similar to independence. As such, this framework was used to import many concepts from classical probability theory to the theory of operator algebras, hence bringing new ideas to solve different problems related with von Neumann algebras and freeness.
This course will introduce and discuss many concepts from classical probability and their analogue in free probability: random variables, freeness, convolution, relation with random matrices, stochastic calculus, entropy and large deviations... We will finally discuss some applications to von Neumann algebras.
Grading will be based on attendency and the presentation of a research paper.
T-T 1--2:30, E17-129
Office hours: Tuesday 2:30--4:30.