Georgia Institute of Technology College of Sciences

I will discuss the limit theorems for composition of analytic functions on the upper-half-plane, and the analogies and differences with the limit theorems for sums of independent random variables. The analogies are enhanced by recalling that the probabilistic limit theorems are really results about convolution of probability measures, and by introducing a new binary operation on probability measures, the monotone convolution.This is joint work with John D. Williams.