Free probability, random matrices, and non-commutative rational functions

In free probability we want to understand the distribution of functions in non-commuting variables. I will explain what this means and what we actually calculate. In particular, the variables will typically be random matrices or operators on Hilbert spaces and a prominent class of functions will be given by non-commutative rational functions.

For this talk, no prior knowledge on operator algebras or random matrices or free probability is assumed.