---
_id: '1677'
abstract:
- lang: eng
  text: 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.
article_number: '103301'
article_processing_charge: No
arxiv: 1
author:
- first_name: Johannes
  full_name: Alt, Johannes
  id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
  last_name: Alt
citation:
  ama: Alt J. The local semicircle law for random matrices with a fourfold symmetry.
    <i>Journal of Mathematical Physics</i>. 2015;56(10). doi:<a href="https://doi.org/10.1063/1.4932606">10.1063/1.4932606</a>
  apa: Alt, J. (2015). The local semicircle law for random matrices with a fourfold
    symmetry. <i>Journal of Mathematical Physics</i>. American Institute of Physics.
    <a href="https://doi.org/10.1063/1.4932606">https://doi.org/10.1063/1.4932606</a>
  chicago: Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold
    Symmetry.” <i>Journal of Mathematical Physics</i>. American Institute of Physics,
    2015. <a href="https://doi.org/10.1063/1.4932606">https://doi.org/10.1063/1.4932606</a>.
  ieee: J. Alt, “The local semicircle law for random matrices with a fourfold symmetry,”
    <i>Journal of Mathematical Physics</i>, vol. 56, no. 10. American Institute of
    Physics, 2015.
  ista: Alt J. 2015. The local semicircle law for random matrices with a fourfold
    symmetry. Journal of Mathematical Physics. 56(10), 103301.
  mla: Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold
    Symmetry.” <i>Journal of Mathematical Physics</i>, vol. 56, no. 10, 103301, American
    Institute of Physics, 2015, doi:<a href="https://doi.org/10.1063/1.4932606">10.1063/1.4932606</a>.
  short: J. Alt, Journal of Mathematical Physics 56 (2015).
corr_author: '1'
date_created: 2018-12-11T11:53:25Z
date_published: 2015-10-09T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '09'
department:
- _id: LaEr
doi: 10.1063/1.4932606
ec_funded: 1
external_id:
  arxiv:
  - '1506.04683'
  isi:
  - '000364237000026'
intvolume: '        56'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1506.04683
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '5472'
quality_controlled: '1'
related_material:
  record:
  - id: '149'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: The local semicircle law for random matrices with a fourfold symmetry
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2015'
...