The spectral edge of some random band matrices

• 成果类型: Article
• 署名作者: Sodin, Sasha
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.2223
• 发表日期: 2010
• 页码: 2223-2251
• 关键词: sample covariance-matrix; LARGEST EIGENVALUES; UNIVERSALITY; ensembles; graphs

摘要

We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the band is sufficiently wide (W >> N-5/6). Otherwise, a different limiting distribution appears.