Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.
"Limit theorems in free probability theory. I." Ann. Probab. 36 (1) 54 - 90, January 2008. https://doi.org/10.1214/009117907000000051