article published yes Giorgio Cipolloni author 42198EFA-F248-11E8-B48F-1D18A9856A870000-0002-4901-7992 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Yuanyuan Xu author 7902bdb1-a2a4-11eb-a164-c9216f71aea30000-0003-1559-1205 LaEr department Random matrices beyond Wigner-Dyson-Mehta project We consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge. https://research-explorer.ista.ac.at/download/20328/20947/2026_JourFuncAnalysis_Cipolloni.pdf application/pdfno Elsevier2026 eng 0022-1236 2411.16572 00158317820000110.1016/j.jfa.2025.111180 2901 Cipolloni, Giorgio, et al. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 290, no. 1, 111180, Elsevier, 2026, doi:<a href="https://doi.org/10.1016/j.jfa.2025.111180">10.1016/j.jfa.2025.111180</a>. Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Optimal Decay of Eigenvector Overlap for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2026. <a href="https://doi.org/10.1016/j.jfa.2025.111180">https://doi.org/10.1016/j.jfa.2025.111180</a>. Cipolloni, G., Erdös, L., &#38; Xu, Y. (2026). Optimal decay of eigenvector overlap for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2025.111180">https://doi.org/10.1016/j.jfa.2025.111180</a> Cipolloni G, Erdös L, Xu Y. 2026. Optimal decay of eigenvector overlap for non-Hermitian random matrices. Journal of Functional Analysis. 290(1), 111180. G. Cipolloni, L. Erdös, and Y. Xu, “Optimal decay of eigenvector overlap for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 290, no. 1. Elsevier, 2026. G. Cipolloni, L. Erdös, Y. Xu, Journal of Functional Analysis 290 (2026). Cipolloni G, Erdös L, Xu Y. Optimal decay of eigenvector overlap for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2026;290(1). doi:<a href="https://doi.org/10.1016/j.jfa.2025.111180">10.1016/j.jfa.2025.111180</a> 203282025-09-10T05:46:07Z2026-06-03T13:12:14Z