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

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.

published proceedings

  • Probability Theory and Related Fields

author list (cited authors)

  • Anshelevich, M.

citation count

  • 4

complete list of authors

  • Anshelevich, Michael

publication date

  • October 1999