The linearization of the central limit operator in free probability theory

Details The linearization of the central limit operator in free probability theory The linearization of the central limit operator in free probability theory

1998-10-07

arxiv.org/abs/math/9810047v2

Probab. Theory Relat. Fields 115 (1999) 3, 401-416

Mathematics

Operator Algebras

13 pages; minor revisions; to be published in Probability Theory and Related Fields

Scientific paper

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.

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