Universality for general Wigner-type matrices

• 成果类型: Article
• 署名作者: Ajanki, Oskari H.; Erdos, Laszlo; Krueger, Torben
• 署名单位: Institute of Science & Technology - Austria
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0740-2
• 发表日期: 2017
• 页码: 667-727
• 关键词: local spectral statistics; eigenvalues

摘要

We consider the local eigenvalue distribution of large self-adjoint random matrices with centered independent entries. In contrast to previous works the matrix of variances is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, , converges to a diagonal matrix, , where solves the vector equation that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes.