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2017 Singularities of the density of states of random Gram matrices
Johannes Alt
Electron. Commun. Probab. 22: 1-13 (2017). DOI: 10.1214/17-ECP97


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 $\mathbb{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.


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Johannes Alt. "Singularities of the density of states of random Gram matrices." Electron. Commun. Probab. 22 1 - 13, 2017.


Received: 28 August 2017; Accepted: 2 November 2017; Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 1378.60020
MathSciNet: MR3734102
Digital Object Identifier: 10.1214/17-ECP97

Primary: 60B20
Secondary: 15B52

Keywords: cubic cusp , Dyson equation , general variance profile , Local law , square-root edge

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