The linearization of the central limit operator in free probability theory

• 成果类型: Article
• 署名作者: Anshelevich, M
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050243
• 发表日期: 1999
• 页码: 401-416
• 关键词: free random-variables; free convolution; entropy; LAWS

摘要

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.