Delocalization for a class of random block band matrices

Bao, Zhigang and Erdős, László (2016) Delocalization for a class of random block band matrices. Probability Theory and Related Fields. ISSN 1432-2064

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We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. 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 G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, 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 η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.

Item Type: Article
DOI: 10.1007/s00440-015-0692-y
Uncontrolled Keywords: supersymmetry, Local semicircle law, Random band matrix, delocalization, Green’s function comparison
Subjects: 500 Science > 530 Physics
Research Group: Erdös Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 11 Feb 2016 16:14
Last Modified: 30 Aug 2017 14:29

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