LOCAL LIMIT THEOREMS IN FREE PROBABILITY THEORY

• 成果类型: Article
• 署名作者: Wang, Jiun-Chau
• 署名单位: Queens University - Canada
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP505
• 发表日期: 2010
• 页码: 1492-1506
• 关键词: free random-variables; free convolution; free entropy; information measure; shannons problem; RANDOM MATRICES; MONOTONICITY; superconvergence; semigroup; analogs

摘要

In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands We prove not only the uniform convergence of the densities to the semicircular density but also their L-P-convergence to the same limit for p > 1/2 Moreover, an entropic central limit theorem is obtained as a consequence of the above results