The linearization of the central limit operator in free probability theory
arXiv:math/9810047
Abstract
We interpret the Central Limit Theorem as a fixed point theorem for a certain operator, and consider the problem of linearizing this operator. In classical as well as in free probability theory, we consider two methods giving such a linearization, and interpret the result as a weak form of the CLT. In the classical case the analysis involves dilation operators; in the free case more general composition operators appear.
13 pages; minor revisions; to be published in Probability Theory and Related Fields