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 [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.
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Received: 3 December 1997
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Anshelevich, M. The linearization of the central limit operator in free probability theory. Probab Theory Relat Fields 115, 401–416 (1999). https://doi.org/10.1007/s004400050243
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DOI: https://doi.org/10.1007/s004400050243
- Mathematical Subject Classification (1991): Primary 46L50; Secondary 60F05, 47B38