article Singularities of the density of states of random Gram matrices published yes Johannes Alt author 36D3D8B6-F248-11E8-B48F-1D18A9856A87 LaEr department Random matrices, universality and disordered quantum systems project For large random matrices X with independent, centered entries but not necessarily identical variances, the eigenvalue density of XX* is well-approximated by a deterministic measure on ℝ. We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities. https://research-explorer.ista.ac.at/download/550/4663/IST-2018-926-v1+1_euclid.ecp.1511233247.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Institute of Mathematical Statistics2017 eng Electronic Communications in Probability 1083-589X 00041638920000110.1214/17-ECP97 22 https://research-explorer.ista.ac.at/record/149 Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63. Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” <i>Electronic Communications in Probability</i>, vol. 22, 63, Institute of Mathematical Statistics, 2017, doi:<a href="https://doi.org/10.1214/17-ECP97">10.1214/17-ECP97</a>. J. Alt, “Singularities of the density of states of random Gram matrices,” <i>Electronic Communications in Probability</i>, vol. 22. Institute of Mathematical Statistics, 2017. Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2017. <a href="https://doi.org/10.1214/17-ECP97">https://doi.org/10.1214/17-ECP97</a>. Alt J. Singularities of the density of states of random Gram matrices. <i>Electronic Communications in Probability</i>. 2017;22. doi:<a href="https://doi.org/10.1214/17-ECP97">10.1214/17-ECP97</a> J. Alt, Electronic Communications in Probability 22 (2017). Alt, J. (2017). Singularities of the density of states of random Gram matrices. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/17-ECP97">https://doi.org/10.1214/17-ECP97</a> 5502018-12-11T11:47:07Z2026-04-08T14:11:36Z