article 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 The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix. https://research-explorer.ista.ac.at/download/1207/5102/IST-2016-722-v1+1_s00220-016-2805-6.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer2017 eng 0010-3616 00039369670000510.1007/s00220-016-2805-6 3493947 - 990 Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990. Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” <i>Communications in Mathematical Physics</i>, vol. 349, no. 3. Springer, pp. 947–990, 2017. Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. <i>Communications in Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a> Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990. Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>. Springer, 2017. <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>. Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:<a href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>. Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. <i>Communications in Mathematical Physics</i>. 2017;349(3):947-990. doi:<a href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a> 12072018-12-11T11:50:43Z2025-07-10T11:50:22Z