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 [VDN92], 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.
Mathematical Subject Classification (1991): Primary 46L50; Secondary 60F05, 47B38
Received: 3 December 1997