Singularities of the density of states of random Gram matrices

Alt, Johannes

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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IST-2018-926-v1+1_euclid.ecp.1511233247.pdf 470.88 KB [Published Version]

DOI

10.1214/17-ECP97

Journal Article | Published | English

Scopus indexed

Author

Alt, Johannes^ISTA

Corresponding author has ISTA affiliation

Department

Erdoes Group

Grant

Random matrices, universality and disordered quantum systems

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

2017

Date Published

2017-11-21

Journal Title

Electronic Communications in Probability

Publisher

Institute of Mathematical Statistics

Volume

Article Number

ISSN

1083589X

IST-REx-ID

550

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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