A generalization of the Lindeberg principle

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000575
• 发表日期: 2006
• 页码: 2061-2076
• 关键词: last-passage percolation; RANDOM MATRICES; UNIVERSALITY; THEOREM

摘要

We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions of exchangeable random variables. This theorem allows us to identify, for the first time, the limiting spectral distributions of Wigner matrices with exchangeable entries.