The random matrix hard edge: rare events and a transition

Diane Holcomb

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arXiv · 1610.05367

The random matrix hard edge: rare events and a transition

Diane Holcomb

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Abstract

We study probabilities of various rare events for the limiting point process that appears at the random matrix hard edge. We also show a transition from hard edge to bulk behavior. Asymptotic events studied include a central limit theorem and large deviation result for the number of points in a growing interval $[0,\lambda]$ as $\lambda \to \infty$. We study these results for the square root of the hard edge process. In this setting many of these behaviors mimic those of the Sine$_\beta$ process.

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Diane Holcomb. 2016-10-17. The random matrix hard edge: rare events and a transition. https://arxiv.org/abs/1610.05367

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