Delocalization for a class of random block band matrices

• 成果类型: Article
• 署名作者: Bao, Zhigang; Erdos, Laszlo
• 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/s00440-015-0692-y
• 发表日期: 2017
• 页码: 673-776
• 关键词: local semicircle law; sigma-model; disordered system; n-orbitals; UNIVERSALITY; localization; diffusion; superbosonization; statistics; dimensions

摘要

We consider Hermitian random matrices H consisting of blocks of size . The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green's function satisfy the local semicircle law with spectral parameter down to the real axis for any , using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466-499, 2014) and the Green's function comparison strategy. Previous estimates were valid only for . The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.