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Singularities of the density of states of random Gram matrices (1708.08442v2)

Published 28 Aug 2017 in math.PR, math-ph, and math.MP

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 $\mathbb{R}$. 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.

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