|Location:||MSRI: Simons Auditorium|
In this lecture we will explore the notion of free independence by looking for analogues of limit theorems from classical probability theory. The R-transform, which is the free analogue of the logarithm of the Laplace transform, is introduced and used to prove the free central limit theorem. The free analogue of the Poisson distribution will also be derived. If time permits, I will outline the classification of compactly supported free infinitely divisible probability measures on the real line (free Levy-Khintchine formula).