The linearization of the central limit operator in free probability theory Academic Article

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.

authors

• Anshelevich, Michael

published proceedings

• PROBABILITY THEORY AND RELATED FIELDS

author list (cited authors)

• Anshelevich, M.

citation count

• 6

complete list of authors

• Anshelevich, M

publication date

• January 1999

publisher

• Springer Nature  Publisher

published in

• Probability Theory and Related Fields  Journal

Digital Object Identifier (DOI)

• 10.1007/s004400050243

start page

• 401

end page

• 416

volume

• 115

issue

• 3

URL

• http://dx.doi.org/10.1007/s004400050243