article published yes László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Torben H Krüger author 3020C786-F248-11E8-B48F-1D18A9856A870000-0002-4821-3297 Dominik J Schröder author 408ED176-F248-11E8-B48F-1D18A9856A870000-0002-2904-1856 LaEr department Random matrices, universality and disordered quantum systems project We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion. https://research-explorer.ista.ac.at/download/6182/6883/2019_Forum_Erdoes.pdf application/pdfno Cambridge University Press2019 eng 2050-5094 1705.10661 00048884710000110.1017/fms.2019.2 7 https://research-explorer.ista.ac.at/record/6179 Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href="https://doi.org/10.1017/fms.2019.2">10.1017/fms.2019.2</a> L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019). Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a href="https://doi.org/10.1017/fms.2019.2">10.1017/fms.2019.2</a>. Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2019. <a href="https://doi.org/10.1017/fms.2019.2">https://doi.org/10.1017/fms.2019.2</a>. L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press, 2019. Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href="https://doi.org/10.1017/fms.2019.2">https://doi.org/10.1017/fms.2019.2</a> Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8. 61822019-03-28T09:05:23Z2026-07-29T13:46:19Z