Convergence rate for spectral distribution of addition of random matrices

article Convergence rate for spectral distribution of addition of random matrices published yes Zhigang Bao author 442E6A6C-F248-11E8-B48F-1D18A9856A870000-0003-3036-1475 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Kevin Schnelli author 434AD0AE-F248-11E8-B48F-1D18A9856A870000-0003-0954-3231 LaEr department Random matrices, universality and disordered quantum systems project Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum. Academic Press2017 eng Advances in Mathematics 1606.03076 00041215040001010.1016/j.aim.2017.08.028 319251 - 291 Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017. Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics, vol. 319, Academic Press, 2017, pp. 251–91, doi:<a href="https://doi.org/10.1016/j.aim.2017.08.028">10.1016/j.aim.2017.08.028</a>. Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 2017;319:251-291. doi:<a href="https://doi.org/10.1016/j.aim.2017.08.028">10.1016/j.aim.2017.08.028</a> Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291. Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics. Academic Press, 2017. <a href="https://doi.org/10.1016/j.aim.2017.08.028">https://doi.org/10.1016/j.aim.2017.08.028</a>. Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. Academic Press. <a href="https://doi.org/10.1016/j.aim.2017.08.028">https://doi.org/10.1016/j.aim.2017.08.028</a> Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291. 7332018-12-11T11:48:13Z2025-06-04T10:13:45Z