The local semicircle law for random matrices with a fourfold symmetry

J. Alt, Journal of Mathematical Physics 56 (2015).


Journal Article | Published | English
Department
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.
Publishing Year
Date Published
2015-10-09
Journal Title
Journal of Mathematical Physics
Volume
56
Issue
10
Article Number
103301
IST-REx-ID

Cite this

Alt J. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 2015;56(10). doi:10.1063/1.4932606
Alt, J. (2015). The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics, 56(10). https://doi.org/10.1063/1.4932606
Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold Symmetry.” Journal of Mathematical Physics 56, no. 10 (2015). https://doi.org/10.1063/1.4932606.
J. Alt, “The local semicircle law for random matrices with a fourfold symmetry,” Journal of Mathematical Physics, vol. 56, no. 10, 2015.
Alt J. 2015. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 56(10).
Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold Symmetry.” Journal of Mathematical Physics, vol. 56, no. 10, 103301, American Institute of Physics, 2015, doi:10.1063/1.4932606.

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