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The linearization of the central limit operator in free probability theory
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  • Published: October 1999

The linearization of the central limit operator in free probability theory

  • Michael Anshelevich1 

Probability Theory and Related Fields volume 115, pages 401–416 (1999)Cite this article

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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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  1. Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA. e-mail: mashel@math.berkeley.edu, , , , , , US

    Michael Anshelevich

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  1. Michael Anshelevich
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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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  • Issue Date: October 1999

  • DOI: https://doi.org/10.1007/s004400050243

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  • Mathematical Subject Classification (1991): Primary 46L50; Secondary 60F05, 47B38
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