The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities

• 成果类型: Article
• 署名作者: Soshnikov, A
• 署名单位: California Institute of Technology; University of California System; University of California Davis
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160338
• 发表日期: 2000
• 页码: 1353-1370
• 关键词: large random matrices; toeplitz determinants; eigenvalues; fluctuation; FORMULA

摘要

We discuss the CLT for the global and local linear statistics of random matrices from classical compact groups. The main parts of our proofs are certain combinatorial identities, much in the spirit of works by M. Kac and H. Spohn.