Georgia Institute of Technology College of Sciences

The CLT for free random variables was settled by Voiculescu very early in this work on free probability. He used this in turn to prove his main result on aymptotic freeness of independent random matrices. On the other hand, in random matrices, fluctuations can be understood as a second order phenomena. This notion of fluctuations has a conterpart in free probability which is called freenes of second order. I will explain what this is and how one can prove a free CLT result in this context. It is also interesting to point out that this is a nontrivial calculation which begs the same question in the classical context and I will comment on that.