article published yes Johannes Alt author 36D3D8B6-F248-11E8-B48F-1D18A9856A87 LaEr department Random matrices, universality and disordered quantum systems project 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. American Institute of Physics2015 eng 1506.04683 00036423700002610.1063/1.4932606 5610 https://research-explorer.ista.ac.at/record/149 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> 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>. Alt J. 2015. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 56(10), 103301. 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. 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> 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>. J. Alt, Journal of Mathematical Physics 56 (2015). 16772018-12-11T11:53:25Z2026-04-08T14:11:36Z