The local semicircle law for random matrices with a fourfold symmetry Journal Article


Author(s): Alt, Johannes
Article Title: The local semicircle law for random matrices with a fourfold symmetry
Affiliation IST Austria
Abstract: We consider real symmetric and complex Hermitian random matrices with the additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale.
Journal Title: Journal of Mathematical Physics
Volume: 56
Issue 10
ISSN: 1089-7658
Publisher: American Institute of Physics  
Date Published: 2015-10-09
Start Page: Article number: 103301
Sponsor: Partially funded by ERC Advanced Grant RANMAT No. 338804
URL:
DOI: 10.1063/1.4932606
Notes: I am very grateful to László Erdős for drawing my attention to this question, for suggesting the method, and for numerous helpful comments during the preparation of this article. Moreover, I thank Oskari Ajanki and Torben Krüger for useful discussions.
Open access: yes (repository)
IST Austria Authors
  1. Johannes Alt
    5 Alt
Related IST Austria Work