Singularities of the density of states of random Gram matrices
Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63.
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Abstract
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.
Publishing Year
Date Published
2017-11-21
Journal Title
Electronic Communications in Probability
Volume
22
Article Number
63
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IST-REx-ID
Cite this
Alt J. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 2017;22. doi:10.1214/17-ECP97
Alt, J. (2017). Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-ECP97
Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-ECP97.
J. Alt, “Singularities of the density of states of random Gram matrices,” Electronic Communications in Probability, vol. 22. Institute of Mathematical Statistics, 2017.
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.” Electronic Communications in Probability, vol. 22, 63, Institute of Mathematical Statistics, 2017, doi:10.1214/17-ECP97.
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