The linearization of the central limit operator in free probability theory
Operator Algebras
2007-05-23 v2 Probability
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.
Keywords
Cite
@article{arxiv.math/9810047,
title = {The linearization of the central limit operator in free probability theory},
author = {Michael Anshelevich},
journal= {arXiv preprint arXiv:math/9810047},
year = {2007}
}
Comments
13 pages; minor revisions; to be published in Probability Theory and Related Fields