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What is Singularities of the density of states of random Gram matrices about?

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 [arXiv:1606.07353] to the vicinity of these singularities.

Author

Alt, Johannes

Published

2017

Language

EN