A KHINTCHINE DECOMPOSITION FOR FREE PROBABILITY

• 成果类型: Article
• 署名作者: Williams, John D.
• 署名单位: Indiana University System; Indiana University Bloomington
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP677
• 发表日期: 2012
• 页码: 2236-2263
• 关键词: multiplicative free convolution; commuting random-variables; distributions; REGULARITY; THEOREM

摘要

Let mu be a probability measure on the real line. In this paper we prove that there exists a decomposition mu = mu(0) boxed plus mu(1) boxed plus ... boxed plus mu(n) boxed plus ... such that mu(0) is infinitely divisible, and mu(i) is indecomposable for i >= 1. Additionally, we prove that the family of all boxed plus-divisors of a measure mu is compact up to translation. Analogous results are also proven in the case of multiplicative convolution.