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The random matrix hard edge: rare events and a transition
Diane Holcomb · 2016-10-18 · via math.PR updates on arXiv.org

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 $[0,λ]$ as $λ\to \infty$. 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$_β$ process.

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