Size bias and other distributional transforms play an important role in sampling problems.  They are also very useful tools in sharp Normal (and other distributional) approximation, giving slick Stein's method quantitative proofs of Central Limit Theorems.  Recently, Goldstein and Schmook discovered a connection between size bias and infinitely divisible distributions, yielding a new kind of Levy--Khintchine formula for positively supported distributions.

In this talk, I will discuss joint work with Goldstein exploring the free probability analogues of bias transforms, with applications to freely infinitely divisible distributions.  In most cases the classical results are transferable, but with a significant change in perspective required.  Among other things, this approach gives a probabilistic meaning to the (free) Levy--Khintchine measure, and a new result simply characterizing those distributions that are positively freely infinitely divisible.