  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.
